{"id":2590,"date":"2023-05-28T06:30:06","date_gmt":"2023-05-28T06:30:06","guid":{"rendered":"https:\/\/vartmaaninstitutesirsa.com\/?page_id=2590"},"modified":"2024-03-08T02:27:52","modified_gmt":"2024-03-08T02:27:52","slug":"chapter-14-oscillations-class-11-physics-notes","status":"publish","type":"page","link":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/chapter-14-oscillations-class-11-physics-notes\/","title":{"rendered":"Chapter 14 Oscillations class 11 physics notes"},"content":{"rendered":"

Chapter 14 Oscillations class 11 physics notes<\/h1>\n

To free download pdf of Chapter 14 Oscillations class 11 physics notes click on the link given below..<\/p>\n

Chapter 14 Oscillations class 11 physics notes<\/h2>\n

SANDEEP SONI\u2019S PHYSICS<\/span><\/strong>\u00a0<\/span><\/strong>COMPETITION CLASSES<\/span><\/strong>\u00a0\u00a0<\/sub><\/span><\/strong><\/p>\n

\n
\n

(10+1, 10+2, IIT-JEE <\/span><\/strong>(Main & Advance),\u00a0<\/span>NEET, B.Sc.\u00a0<\/span><\/strong>Agriculture<\/span>,\u00a0<\/span>NDA)\u00a0<\/span><\/strong><\/p>\n

OPP:<\/span>\u00a0JHUNTHARA DHARAMSHALA\u00a0<\/span>NEAR SURKHAB CHOWK<\/span>,\u00a0<\/span>HISSAR ROAD SIRSA<\/span>\u00a0<\/span><\/p>\n

\u00a0<\/span>Unit-10: Oscillations and Waves\u00a0<\/span><\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>PH-\u00a0<\/span>94676-12340,<\/span><\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<\/div>\n

\u00a0Unit-10: Oscillations and Waves<\/span><\/u><\/strong><\/p>\n

1 Periodic Motion<\/span><\/u><\/strong>:<\/span><\/u><\/em><\/strong><\/p>\n

A motion of the body which repeats itself after a regular interval of time is called periodic motion.<\/span><\/em><\/p>\n

\uf0fc<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>e.g<\/span><\/em>: The motion of all planets around Sun, motion of Moon around Earth, Motion of bob of pendulum, all are periodic motions.<\/span><\/p>\n

2Oscillatory Motions:<\/span><\/u><\/strong><\/p>\n

If a body moves to and fro about a fixed point, then the motion of the body is called oscillatory motion.<\/span><\/em><\/p>\n

\uf0fc<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>e.g:<\/span><\/em>\u00a0The motion of a bob of simple pendulum, motion of spring is oscillatory motion.<\/span><\/p>\n

\uf046<\/span>\u00a0\u00a0<\/span>Periodic Motion V\/s Oscillatory Motion:<\/span><\/u><\/strong><\/p>\n

All oscillatory motions are periodic motions because they repeats their periods after a regular interval of time but all periodic motions are not oscillatory motions because it is not necessary to vibrate to and fro for periodic motions.<\/span><\/p>\n

3 Periodic Functions:<\/span><\/u><\/strong><\/p>\n

Any functions which repeat itself at a regular interval of time is called periodic functions.<\/span><\/em><\/p>\n

Consider a function\u00a0<\/span>\"\"\u00a0of time period\u00a0<\/span>\"\"\u00a0such that<\/span>\u00a0 <\/span><\/p>\n

\"\"<\/p>\n

So\u00a0<\/span>\"\"\u00a0is periodic function over a time period<\/span>\"\".<\/span><\/p>\n

e.g:-\u00a0<\/span>\"\"\u00a0and\u00a0<\/span>\"\"\u00a0are periodic over a time interval or period\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

as<\/span>\u00a0\u00a0<\/span>\"\"<\/p>\n

And<\/span> \"\"<\/p>\n

Now suppose<\/span>\u00a0\u00a0<\/span>\"\"<\/p>\n

\"\"<\/p>\n

\"\"\u00a0<\/span><\/p>\n

\u27f9<\/span>\"\"<\/p>\n

Similarly\u00a0<\/span>\"\"<\/p>\n

Hence<\/span>\u00a0 \u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

and\u00a0<\/span>\"\"\u00a0are periodic functions.<\/span><\/p>\n

Or we may write<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0<\/span>\"\"<\/p>\n

And<\/span><\/p>\n

\"\"<\/p>\n

4 Harmonic and Non Harmonic Periodic Functions:<\/span><\/u><\/strong><\/p>\n

A periodic function which can be represented by a sine or cosine curve is called harmonic function<\/span><\/em>\u00a0<\/span><\/p>\n

e.g:-\u00a0<\/span>\"\"<\/p>\n

A periodic function which cannot be represented by a sine or cosine is called non harmonic function <\/span><\/p>\n

e.g.:\u00a0 –<\/span>\"\"\u00a0etc.<\/span><\/p>\n

\uf0d8<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>A non harmonic function may be constructed by two or more than two harmonic functions as\u00a0<\/span><\/p>\n

\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

\uf0d8<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>All harmonic functions are periodic but all periodic functions are not harmonic because all periodic functions cannot be represented by sine or cosine functions.<\/span><\/p>\n

5<\/span><\/u><\/strong>\u00a0\u00a0<\/span><\/u><\/strong>Simple Harmonic Motion:<\/span><\/u><\/strong><\/p>\n

If a particle moves to and fro about its mean position then the motion of particle is called simple harmonic motion.<\/span><\/em><\/p>\n

The restoring force in the body is direction proportional to the displacement of the particle from mean position<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0<\/span>i.e.<\/span>\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

Or<\/span>\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

Or<\/span>\u00a0<\/span>\"\"<\/p>\n

Where\u00a0<\/span>\"\"\u00a0is called force constant.<\/span><\/p>\n

Here\u00a0<\/span>\"\"\u00a0sign indicate that restoring force always act in opposite to displacement of the body.<\/span><\/p>\n

Now from Newton\u2019s second law<\/span><\/p>\n

\"\"<\/p>\n

\u27f9<\/span>\u00a0<\/span>\"\"<\/p>\n

Or<\/span>\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

Hence\u00a0<\/span>in S.H.M., acceleration produced in the body is directly proportionality to displacement of the body<\/span><\/em>.<\/span><\/p>\n

\u00a0<\/span><\/u><\/strong>Example of S.H.M:<\/span><\/u><\/strong><\/p>\n

    \n
  • \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Oscillations of a loaded spring.<\/li>\n
  • \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Vibration of a tuning fork.<\/li>\n
  • \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Oscillation of a bob of simple pendulum.<\/li>\n<\/ul>\n

    6<\/span><\/u><\/em><\/strong>\u00a0\u00a0<\/span><\/u><\/em><\/strong>Differential Equation for S.H.M.:<\/span><\/u><\/strong><\/p>\n

    In S.H.M. the restoring force acting on the particle may be given as<\/span><\/p>\n

    \u00a0<\/span>\"\"<\/p>\n

    Where\u00a0<\/span>\"\"\u00a0is spring constant and\u00a0<\/span>\"\"\u00a0is displacement<\/span><\/p>\n

    Now from Newton second law of motion.<\/span><\/p>\n

    \"\"<\/p>\n

    \u27f9<\/span>\u00a0<\/span>Comparing eq. (i) and (ii) we get<\/span>\u00a0\u00a0<\/span><\/p>\n

    \u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

    Or<\/span>\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

    Or<\/span>\u00a0\u00a0\u00a0<\/span>\"\"<\/p>\n

    Putting\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

    we get\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

    Or<\/span>\u00a0<\/span>\"\"<\/p>\n

    The above eq. is called differential eq. of S.H.M.<\/span><\/p>\n

    The solution of above eq. is<\/span><\/p>\n

    \u00a0<\/span>\"\"<\/p>\n

    Where\u00a0<\/span>\"\"\u00a0is amplitude,\u00a0<\/span>\"\"\u00a0is phase angle,<\/span>\"\"\u00a0is initial phase or epoch.<\/span><\/p>\n

    This can be proven as\u00a0<\/span><\/p>\n

    \"\"<\/p>\n

    Then\u00a0<\/span>\"\"<\/p>\n

    And<\/span>\u00a0<\/span>\"\"<\/p>\n

    \u27f9<\/span>\u00a0<\/span>\"\"<\/p>\n

    Which is same as eq. (iii) hence solution of eq. (iii) is<\/span><\/p>\n

    \u00a0<\/span>\"\"<\/p>\n

    7 Time Period of S.H.M.:<\/span><\/u><\/strong><\/p>\n

    If we replace\u00a0<\/span>\"\"\u00a0by\u00a0<\/span>\"\"\u00a0in eq.<\/span><\/p>\n

    \u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

    then we get<\/span>\u00a0\u00a0<\/span><\/em><\/strong>\"\"<\/p>\n

    \"\"\u00a0<\/span><\/p>\n

    \"\"<\/p>\n

    Thus time period of S.H.M. is\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

    Or<\/span>\u00a0<\/span>\"\"\u00a0<\/span>\u00a0<\/span>\u00a0<\/span>\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

    Or<\/span>\u00a0<\/span>\"\"<\/p>\n

    8 Some Important Terms Connected with S.H.M:<\/span><\/u><\/strong><\/p>\n

      \n
    1. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Harmonic oscillator:<\/u><\/li>\n<\/ol>\n

      \u00a0<\/span>A\u00a0<\/span>particle executing simple harmonic motion is called harmonic oscillator<\/span><\/em>.<\/span><\/p>\n

        \n
      1. Displacement:<\/u><\/li>\n<\/ol>\n

        The displacement of oscillating particle from its mean position at any instant of<\/span><\/em>\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/em>time is called displacement of the particle. It is denoted by<\/span><\/em>\u00a0\u00a0<\/span><\/em>\"\"\u00a0or<\/span><\/em>\"\".<\/span><\/em><\/p>\n

          \n
        • Amplitude:<\/u><\/li>\n<\/ul>\n

          The maximum displacement of the particle from mean position is called amplitude. It is denoted by\u00a0<\/span><\/em>\"\".<\/span><\/p>\n

            \n
          • Oscillation or Cycle:<\/u><\/li>\n<\/ul>\n

            One complete back and forth motion of particle starting and ending at same point is called one oscillation or one cycle one vibration<\/span><\/em>.<\/span><\/p>\n

              \n
            • Time Period:<\/u><\/li>\n<\/ul>\n

              The time taken by the particle to complete one cycle is called time period. It is denoted by T<\/span><\/em><\/p>\n

                \n
              • Frequency:<\/u><\/li>\n<\/ul>\n

                The number of oscillations completed unit time is called frequency<\/span><\/em>. It is denoted by\u00a0<\/span>\"\"<\/p>\n

                Unit:\u00a0<\/span>\"\"<\/p>\n

                (Vii) Angular Frequency:<\/span><\/u><\/strong><\/p>\n

                A quantity obtained by multiplying frequency\u00a0<\/span><\/em>\"\"\u00a0by a factor\u00a0<\/span><\/em>\"\"\u00a0is called angular frequency. It is denoted by\u00a0<\/span><\/em>\"\".<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

                Thus\u00a0<\/span>\"\"<\/p>\n

                Unit:-\u00a0<\/span>\"\"<\/p>\n

                9 Phase:<\/span><\/u><\/strong><\/p>\n

                The phase of a particle at any instant gives the state of the particle w.r.t. its position and direction of motion at that instant. It is denoted by\u00a0<\/span><\/em>\"\".<\/span><\/em><\/p>\n

                For a simple harmonic eq.<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

                \"\"<\/p>\n

                The phase of the particle is<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                \u00a0<\/span>\"\"<\/p>\n

                The phase of the particle at\u00a0<\/span>\"\"\u00a0is called its\u00a0<\/span>initial phase or epoch.<\/span><\/em><\/p>\n

                \u00a0<\/span><\/em>i.e.<\/span>\u00a0<\/span>At<\/span>\u00a0<\/span>\"\"\u00a0,<\/span><\/em>\u00a0\u00a0\u00a0<\/span><\/em>\"\"<\/p>\n

                Thus\u00a0<\/span>\"\"\u00a0is initial phase or epoch.<\/span><\/p>\n

                10 Uniform Circular Motion and S.H.M.:<\/span><\/u><\/strong><\/p>\n

                Suppose a particle\u00a0<\/span>\"\"\u00a0moving in a circle of radius<\/span>\"\". At any time suppose particle make angle\u00a0<\/span>\"\"\u00a0with\u00a0<\/span>\"\"\u00a0and\u00a0<\/span>\"\"\u00a0is foot of\u00a0<\/span>\u22a5<\/span>\u00a0drawn from\u00a0<\/span>\"\"\u00a0to<\/span>\"\". Now when particle move from\u00a0<\/span>\"\"\u00a0to\u00a0<\/span>\"\"\u00a0then\u00a0<\/span>\"\"\u00a0to\u00a0<\/span>\"\"\u00a0then\u00a0<\/span>\"\"\u00a0to\u00a0<\/span>\"\"\u00a0then\u00a0<\/span>\"\"\u00a0\u00a0<\/span>to\u00a0<\/span>\"\". In all cases the\u00a0<\/span>\"\"\u00a0oscillate about mean position\u00a0<\/span>\"\"\u00a0on\u00a0<\/span>\"\"\u00a0axis. Thus uniform circular motion also exhibits S.H.M. or\u00a0<\/span>simple harmonic motion may be defined as the projection of uniform circular motion upon a diameter of the circle.<\/span><\/em><\/p>\n

                Displacement in Simple Harmonic Motion:<\/span><\/u><\/strong><\/p>\n

                As from diagram\u00a0<\/span>\"\"<\/p>\n

                In right angle\u00a0<\/span>\u00a0<\/span><\/p>\n

                \u2206 ONP<\/span>\u00a0\u00a0\u00a0<\/span>\"\"\u00a0<\/span>\u00a0<\/span><\/p>\n

                Where\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

                Or<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>\"\"<\/p>\n

                Or\u00a0<\/span>\u00a0<\/span>\"\"\u00a0\u00a0<\/span><\/p>\n

                \u27f9<\/span>\u00a0displacement\u00a0<\/span>\"\"<\/p>\n

                If point A lies below the x axis\u00a0<\/span><\/p>\n

                then\u00a0<\/span>\"\"\u00a0\u00a0<\/span><\/p>\n

                \u27f9<\/span>\u00a0<\/span>\"\"<\/p>\n

                Here\u00a0<\/span>\"\"\u00a0is the initial phase of S.H.M.<\/span><\/p>\n

                Q.\u00a0<\/span><\/strong>\u00a0<\/span><\/strong>Show that\u00a0<\/span><\/strong>\"\"\u00a0represents S.H.M.<\/span><\/strong><\/p>\n

                Sol.\u00a0<\/span><\/em><\/strong>As<\/span><\/em>\u00a0\u00a0<\/span><\/em>\"\"<\/p>\n

                Differentiating w.r.t. time\u00a0<\/span>\"\", we get<\/span>\u00a0\u00a0<\/span><\/p>\n

                \u00a0<\/span><\/em>\"\"<\/p>\n

                Again differentiating w.r.t. time\u00a0<\/span>\"\",\u00a0<\/span><\/p>\n

                we get<\/span>\u00a0\u00a0<\/span>\"\"<\/p>\n

                \"\"<\/p>\n

                Or<\/span>\u00a0\u00a0\u00a0<\/span>\u00a0<\/span><\/em>\"\"<\/p>\n

                Or<\/span>\u00a0\u00a0<\/span>\u00a0<\/span><\/em>\"\"<\/p>\n

                Which is the eq. for S.H.M. Hence\u00a0<\/span>\"\"\u00a0represents S.H.M.<\/span><\/p>\n

                11 Velocity in S.H.M.:<\/span><\/u><\/strong><\/p>\n

                As we know that rate of change of displacement of a particle represent velocity. So we can calculate velocity by differentiating displacement.<\/span><\/p>\n

                As displacement of the particle having S.H.M. can be given as<\/span>\u00a0\u00a0<\/span><\/p>\n

                \u00a0<\/span>\"\"<\/p>\n

                Differentiating w.r.t. time we get<\/span>\u00a0\u00a0<\/span><\/p>\n

                \u00a0\u00a0<\/span>\"\"\u00a0\u00a0\u00a0<\/span><\/p>\n

                Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                Or<\/span>\u00a0<\/span>\"\"\u00a0<\/span>\u00a0<\/span>\u00a0<\/span>\u00a0<\/span>\"\"<\/p>\n

                Special Cases:<\/span><\/u><\/strong><\/p>\n

                  \n
                1. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>When particle is at mean position<\/li>\n<\/ol>\n

                  \u00a0<\/span>then\u00a0<\/span>\u00a0<\/span>\"\"\u00a0\u00a0\u00a0<\/span>\u27f9<\/span>\u00a0<\/span>\"\"<\/p>\n

                    \n
                  1. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>When particle is at extreme position then<\/li>\n<\/ol>\n

                    \u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>\u27f9<\/span>\u00a0<\/span>\"\"<\/p>\n

                    Hence velocity at extreme position is zero.<\/span><\/p>\n

                    12 Acceleration of the Particle Having S.H.M.:<\/span><\/u><\/strong><\/p>\n

                    As we know the rate of change of velocity of a particle is called acceleration. So by differentiating velocity of the particle w.r.t. time we can obtain acceleration.<\/span><\/p>\n

                    Here in S.H.M. the velocity of the particle can be given as\u00a0<\/span><\/p>\n

                    \u00a0<\/span>\"\"<\/p>\n

                    Differentiating w.r.t. time we get<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

                    \"\"\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                    Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                    Or<\/span>\u00a0<\/span>\u00a0\u00a0<\/span>\"\"\u00a0\u00a0\u00a0<\/span><\/p>\n

                    \u00a0<\/span>Here\u00a0<\/span>\"\"\u00a0sign indicate that acceleration produced in the particle will oppose the displacement of the particle<\/span><\/em>.<\/span><\/p>\n

                    Special Cases:<\/span><\/u><\/strong><\/p>\n

                      \n
                    • When particle is at mean position then<\/li>\n<\/ul>\n

                      \u00a0<\/span><\/em>\"\"\u00a0<\/span><\/em>\u00a0<\/span><\/em>\u27f9<\/span><\/em>\u00a0<\/span><\/em>\"\"\u00a0<\/span><\/em><\/p>\n

                      \u00a0acceleration of the particle at mean position is zero.<\/span><\/em><\/p>\n

                        \n
                      • When particle is at extreme position then<\/li>\n<\/ul>\n

                        \"\"\u00a0<\/span><\/em>\u00a0<\/span><\/em>\u27f9<\/span><\/em>\u00a0<\/span><\/em>\"\".\u00a0<\/span><\/em><\/p>\n

                        acceleration of the particle at extreme position is maximum.<\/p>\n

                        \u00a0<\/span><\/em><\/strong>13\u00a0<\/span><\/u><\/em><\/strong>Phase Relationship between Displacement, Velocity and Acceleration:<\/span><\/u><\/strong><\/p>\n

                        Graphical relationship between displacement, velocity and acceleration of particle having S.H.M. is<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                        \"\"<\/p>\n

                        \"\"<\/p>\n

                        And<\/span>\u00a0<\/span>\"\"<\/p>\n

                        The variation of\u00a0<\/span>\"\"\u00a0and\u00a0<\/span>\"\"\u00a0with respect to time may be given by<\/span><\/p>\n\n\n\n\n\n\n
                        \n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n<\/tr>\n

                        \n

                        \"\")<\/span><\/strong><\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n<\/tr>\n

                        \n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n<\/tr>\n

                        \n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n

                        		\n

                        \"\"<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                        Now we can plot a graph between t and A for displacement, velocity and acceleration as below:\u00a0<\/span><\/p>\n

                        Conclusion:<\/span><\/strong><\/p>\n

                          \n
                        1. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Displacement, velocity and acceleration all vary harmonically w.r.t. time.<\/li>\n
                        2. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>The amplitude of velocity and acceleration are \"\"\u00a0and \"\"\u00a0times respectively for displacement.<\/li>\n
                        3. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Velocity leads displacements by phase angle \"\".<\/li>\n
                        4. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Acceleration leads displacement by phase angle \u03c0. Also when displacement is maximum the acceleration is minimum and vice versa. But when displacement is zero then acceleration is also zero.<\/li>\n<\/ol>\n

                          14 Energy in S.H.M.: Kinetic and Potential Energy:<\/span><\/u><\/strong><\/p>\n

                          There are two types of energy associated with S.H.M., Kinetic energy and potential energy both may be calculated as given below:<\/span><\/p>\n

                            \n
                          1. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span>Kinetic Energy:<\/u><\/li>\n<\/ol>\n

                            As we know the displacement of the particle having S.H.M. is\u00a0<\/span><\/p>\n

                            \u00a0<\/span>\"\"<\/p>\n

                            So velocity<\/span> \u00a0<\/span>\"\"<\/p>\n

                            Hence Kinetic energy<\/span><\/p>\n

                            \u00a0<\/span>\"\"<\/p>\n

                            Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                            \"\"<\/p>\n

                            \"\"\u00a0<\/span>\"\"<\/p>\n

                              \n
                            • Potential Energy:<\/u><\/li>\n<\/ul>\n

                              As we know the displacement x of the particle from its mean position on is directly proportional to force acting on it as<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                              \u00a0\u00a0<\/span>\"\"<\/p>\n

                              Now small amount of work is to be done to move particle small distance\u00a0<\/span>\"\"\u00a0as<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>\"\"<\/p>\n

                              So total work done<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                              \u00a0<\/span>\"\"<\/p>\n

                              This work is store in body in form of P.E. so<\/span>\u00a0\u00a0<\/span><\/p>\n

                              \u00a0\u00a0<\/span>\"\"<\/p>\n

                              \"\"<\/p>\n

                              Total Energy:<\/span><\/u><\/strong><\/p>\n

                              The sum of Kinetic energy and potential energy is called total energy of a harmonic oscillator as given below:<\/span><\/p>\n

                              \"\"<\/p>\n

                              Or<\/span>\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

                              Hence total energy of a harmonic oscillator is independent of time or displacement, it is conserved.<\/span><\/p>\n

                              15 Graphically Representation:<\/span><\/u><\/strong><\/p>\n

                              At mean position<\/span><\/strong>\u00a0i.e.\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

                              Total energy\u00a0<\/span>\"\"<\/p>\n

                              Kinetic energy\u00a0<\/span>\"\"<\/p>\n

                              Potential energy\u00a0<\/span>\"\"<\/p>\n

                              At extreme position<\/span><\/strong>\u00a0i.e.\u00a0<\/span>\"\"<\/p>\n

                              Kinetic energy\u00a0<\/span>\"\"<\/p>\n

                              Potential energy\u00a0<\/span>\"\"<\/p>\n

                              Thus sum of K.E. and P.E. remains conserved.\u00a0<\/span><\/p>\n

                              Example<\/strong>\u00a0\u00a0<\/strong>A particle of mass 40 g executes a simple harmonic motion of amplitude 2.0 cm.<\/strong>\u00a0\u00a0<\/strong>If the time period is 0.20 s, find the total mechanical energy of the system.\u00a0<\/strong><\/p>\n

                              Solution: The total mechanical energy of the system is<\/p>\n

                              \u00a0\"\"<\/p>\n

                              \"\"<\/p>\n

                              Example<\/strong>\u00a0\u00a0<\/strong>A particle of mass 0.50 kg executes a simple harmonic motion under a force F = – (50 N\/m)x.<\/strong>\u00a0\u00a0<\/strong>If it crosses the centre of oscillation with a speed of<\/strong>\u00a0\u00a0<\/strong>10 m\/s,<\/strong>\u00a0\u00a0<\/strong>find the amplitude of the motion.\u00a0<\/strong><\/p>\n

                              Solution:\u00a0 The kinetic energy of the particle when it is at the centre of oscillation is<\/p>\n

                              \u00a0\"\"<\/p>\n

                              \"\"<\/p>\n

                              The potential energy is zero here.<\/p>\n

                              At the maximum displacement x = A,<\/p>\n

                              the speed is zero and hence the kinetic energy is zero.<\/p>\n

                              The potential \"\"\u00a0, as there is no loss of energy,<\/p>\n

                              \u00a0\"\"<\/p>\n

                              The force on the particle is given<\/p>\n

                              By \"\"<\/p>\n

                              Thus, the spring constant is k = 50 N\/m.<\/p>\n

                              Equation (i) gives<\/p>\n

                              \"\"<\/p>\n

                              or,\u00a0 A = 1 m.<\/p>\n

                              16 Oscillation due to a Spring:<\/span><\/u><\/strong><\/p>\n

                                \n
                              1. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>Horizontal Oscillations of Body on Spring:<\/u><\/li>\n<\/ol>\n

                                Suppose a mass less spring whose one end is fixed and other end is stretched to a distance\u00a0<\/span>\"\"\u00a0from equilibrium position then restoring force developed in spring is\u00a0<\/span>\"\"<\/p>\n

                                Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                Thus spring will execute S.H.M.\u00a0<\/span><\/em><\/p>\n

                                Now time period of oscillation is<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

                                \u00a0<\/span>\"\"\u00a0\u00a0\u00a0<\/span><\/p>\n

                                Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                And frequency of oscillation<\/span><\/p>\n

                                \u00a0<\/span>\"\"<\/p>\n

                                Thus\u00a0<\/span>smaller the time period larger will be the frequency of oscillation. Also for smaller body the time period will be small and frequency will be large<\/span><\/em>.<\/span><\/p>\n

                                  \n
                                • Vertical<\/u>\u00a0\u00a0<\/u>Oscillation of a body on a Spring:<\/u><\/li>\n<\/ul>\n

                                  If a spring is suspended vertically and a body of mass\u00a0<\/span>\"\"\u00a0is attached to its lower end then spring get stretched to a distanced due to the weight of the body.<\/span><\/p>\n

                                  If the body is pulled vertically downward through a small distance\u00a0<\/span>\"\"\u00a0from its equilibrium position and then released. Then restoring force developed in the spring may be given by\u00a0<\/span><\/p>\n

                                  \"\"<\/p>\n

                                  Here<\/span>\u00a0<\/span>\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                  So<\/span>\u00a0<\/span>\"\"<\/p>\n

                                  If\u00a0<\/span>\"\"\u00a0is the amount of acceleration in the body,\u00a0<\/span><\/p>\n

                                  then<\/span>\u00a0\u00a0\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                  Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                  Or<\/span>\u00a0<\/span>\"\"\u00a0<\/span>\u00a0<\/span>\"\"<\/p>\n

                                  Hence body execute S.H.M. and hence its time period may be given as<\/span>\u00a0\u00a0<\/span><\/p>\n

                                  \u00a0<\/span>\"\"<\/p>\n

                                  Or<\/span>\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

                                  Here\u00a0<\/span>clearly shown that acceleration due to gravity does not effects the time period of the oscillation of the particle.<\/span><\/em><\/p>\n

                                    \n
                                  1. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span>Oscillation of Loaded Spring Combination:<\/u><\/li>\n
                                  2. \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Spring Connected in parallel:<\/u><\/strong><\/li>\n<\/ol>\n

                                    In fig. (a) and (b) two spring of spring constants\u00a0<\/span>\"\"\u00a0and\u00a0<\/span>\"\"\u00a0are connected in parallel. Let\u00a0<\/span>\"\"\u00a0is the extension produced in each spring then restoring force developed in the springs may be given as\u00a0<\/span><\/p>\n

                                    \"\"\u00a0\u00a0<\/span>\u00a0<\/span>and<\/span>\u00a0\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

                                    So the total restoring force in parallel combinations of spring is<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                    \u00a0\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

                                    Now let\u00a0<\/span>\"\"\u00a0\u00a0<\/span>is the force constant in parallel combination\u00a0<\/span><\/p>\n

                                    then<\/span>\u00a0\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                    Or\u00a0<\/span>\u00a0<\/span>\"\"<\/p>\n

                                    So the frequency of vibrations of the parallel combination is<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

                                    \u00a0<\/span>\"\"<\/p>\n

                                      \n
                                    • \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>If Spring are connected in series:<\/u><\/li>\n<\/ul>\n

                                      In fig. (c) and (d) two springs of spring constants\u00a0<\/span>\"\"\u00a0and\u00a0<\/span>\"\"\u00a0are connected in series and suppose\u00a0<\/span>\"\"\u00a0and\u00a0<\/span>\"\"\u00a0are the extension produce in the springs.<\/span><\/p>\n

                                      Then restoring forces developed in spring is<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

                                      \u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>and<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>\"\"<\/p>\n

                                      Or<\/span>\u00a0<\/span>\"\"\u00a0\u00a0<\/span>\u00a0<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>and<\/span>\u00a0\u00a0\u00a0<\/span>\"\"<\/p>\n

                                      But in series combination<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>\"\"\u00a0\u00a0<\/span><\/p>\n

                                      So total extension<\/span><\/p>\n

                                      \u00a0<\/span>\"\"<\/p>\n

                                      Or<\/span>\u00a0\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                      Or\u00a0<\/span>\u00a0<\/span>\"\"<\/p>\n

                                      If\u00a0<\/span>\"\"\u00a0is force constant for series combination<\/span><\/p>\n

                                      \u00a0<\/span>then<\/span>\u00a0\u00a0<\/span>\"\"\u00a0\u00a0<\/span><\/p>\n

                                      \u27f9<\/span>\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                      Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                      \u2234<\/span>\u00a0<\/span>The frequency of vibration for series combination is<\/span><\/p>\n

                                      \u00a0\u00a0<\/span>\"\"<\/p>\n

                                      Example<\/strong>\u00a0\u00a0<\/strong>A particle of mass 200 g executes a simple harmonic motion. The restoring force is provided by a spring of spring constant 80 N\/m.<\/strong>\u00a0\u00a0<\/strong>Find the time period.\u00a0<\/strong><\/p>\n

                                      Solution:\u00a0 The time period is<\/p>\n

                                      \u00a0\"\"<\/p>\n

                                      \"\"<\/p>\n

                                      17 Simple Pendulum:<\/span><\/u><\/strong><\/p>\n

                                      A simple pendulum is consists of point mass suspended by a\u00a0<\/span><\/em>flexible, inelastic and weightless<\/span><\/u><\/em>\u00a0string from a rigid support of\u00a0<\/span><\/em>infinite mass<\/span><\/u><\/em>. In practical, we can neither have a point mass nor a weightless string so\u00a0<\/span><\/em>no pendulum is an ideal simple pendulum<\/span><\/u><\/em>.<\/span><\/em><\/p>\n

                                      Expression for Simple Pendulum:<\/span><\/u><\/strong><\/p>\n

                                      Suppose at any time\u00a0<\/span>\"\"\u00a0the bob of simple pendulum lies at point<\/span>\"\". At\u00a0<\/span>\"\"\u00a0the weight of the bob acts in downward direction. Now resolving\u00a0<\/span>\"\"\u00a0into rectangular components we get\u00a0<\/span><\/p>\n

                                      \"\"<\/p>\n

                                      Where T is the tension in the strings and\u00a0<\/span>\"\"\u00a0brings the bob toward mean position and act as restoring force as\u00a0<\/span><\/p>\n

                                      \"\"<\/p>\n

                                      When \u03b8 is small then we can write\u00a0<\/span>\"\"\u00a0<\/span><\/p>\n

                                      \"\"<\/p>\n

                                      Also<\/span>\u00a0<\/span>\"\"<\/p>\n

                                      Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                      Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                      Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                      Clearly\u00a0<\/span>\"\"<\/p>\n

                                      Now time period of simple pendulum is\u00a0<\/span><\/p>\n

                                      \"\"\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                      Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                      \uf0d8<\/span>\u00a0\u00a0\u00a0\u00a0<\/span>Thus time of a simple pendulum depends upon length, acceleration due to gravity\u00a0<\/span><\/em>\"\"\u00a0and independent of mass\u00a0<\/span><\/em>\"\"\u00a0of the bob.<\/span><\/em><\/p>\n

                                      Example<\/strong>\u00a0\u00a0<\/strong>Calculate the time period of a simple pendulum of length one meter. The acceleration due to gravity at the place is\u00a0<\/strong>\"\"\u00a0<\/strong><\/p>\n

                                      Solution :\u00a0 The time period is<\/p>\n

                                      \u00a0\"\"<\/p>\n

                                      Example<\/strong>\u00a0\u00a0<\/strong>In a laboratory experiment with simple pendulum it was found that it took<\/strong>\u00a0\u00a0<\/strong>36 s to complete 20<\/strong>\u00a0\u00a0<\/strong>oscillations when the effective length was kept at<\/strong>\u00a0\u00a0<\/strong>80 cm.<\/strong>\u00a0\u00a0<\/strong>Calculate the acceleration due to gravity from these data.<\/strong>\u00a0\u00a0<\/strong><\/p>\n

                                      Solution:\u00a0 The time period of a simple pendulum is given by<\/p>\n

                                      \u00a0\"\"<\/p>\n

                                      or\u00a0 \"\"<\/p>\n

                                      In the experiment described in the question, the time period is<\/p>\n

                                      \u00a0\"\"<\/p>\n

                                      Thus, by (i),<\/p>\n

                                      \"\"<\/p>\n

                                      18 Other Example of S.H.M.:<\/span><\/u><\/strong><\/p>\n

                                        \n
                                      • \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Oscillation of a liquid Column in a U-Tube:<\/u><\/li>\n<\/ul>\n

                                        Suppose a U-tube of cross section A contains a liquid of density \u03c1 up to a height<\/span>\"\". Then mass of the liquid in U-tube is\u00a0<\/span><\/p>\n

                                        \u00a0<\/span>\"\"<\/p>\n

                                        If liquid is depressed at one side then restoring force develop in liquid i.e.<\/span>\u00a0\u00a0<\/span>\"\"<\/p>\n

                                        \u00a0\u00a0<\/span>Or<\/span>\u00a0<\/span>\"\"<\/p>\n

                                        i.e.<\/span>\u00a0<\/span>\u00a0<\/span>\"\"<\/p>\n

                                        Thus force on the liquid is proportional to displacement and acts in its opposite direction; hence the liquid in U-tube executes S.H.M. with force constant<\/span>\u00a0\u00a0<\/span>\"\"<\/p>\n

                                        The time period of oscillation is\u00a0<\/span><\/p>\n

                                        \"\"<\/p>\n

                                        If\u00a0<\/span>\"\"\u00a0is the length of the liquid column, then<\/span><\/p>\n

                                        \"\"\u00a0\u00a0\u00a0<\/span>and<\/span>\u00a0\u00a0<\/span>\"\"<\/p>\n

                                          \n
                                        • \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Oscillation of Body Dropped in a Tunnel Along the Diameter of Earth:<\/u><\/li>\n<\/ul>\n

                                          Suppose earth is a sphere of radius\u00a0<\/span>\"\" and Centre\u00a0<\/span>\"\". again suppose that a pipe is drug along the diameter of the earth. Again suppose that a body of mass\u00a0<\/span>\"\"\u00a0is dropped in to the tunnel and is at point P which is at a depth d below the surface of earth.<\/span><\/p>\n

                                          If\u00a0<\/span>\"\"\u00a0is the acceleration due to gravity at\u00a0<\/span>\"\"\u00a0then<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                          \u00a0\u00a0<\/span>\"\"<\/p>\n

                                          If\u00a0<\/span>\"\"\u00a0is the displacement of the body from centre of the earth then<\/span>\u00a0\u00a0\u00a0<\/span><\/p>\n

                                          \u00a0<\/span>\"\"\u00a0<\/span>\u27f9<\/span>\u00a0<\/span>\"\"<\/p>\n

                                          Now force acting on the body is<\/span>\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                          \u00a0<\/span>\"\"<\/p>\n

                                          Or<\/span>\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                          Or<\/span>\u00a0<\/span>\"\"\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                          where<\/span>\u00a0\u00a0\u00a0<\/span>\"\"<\/p>\n

                                          Hence the displacement of the body is directly proportional to restoring force or applied force. Hence body will execute S.H.M. with time period of oscillation<\/span>\u00a0\u00a0\u00a0<\/span>\"\"<\/p>\n

                                          \"\"<\/p>\n

                                          19 Free, Damped and Maintained Oscillation:<\/span><\/u><\/strong><\/p>\n

                                            \n
                                          • \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>Un-damped or Free Oscillation:\u00a0<\/u><\/li>\n<\/ul>\n

                                            If amplitude of oscillating particle does not changes with respect to time then the oscillation of particle is said to be free or un-damped oscillation.\u00a0<\/span><\/p>\n

                                            e.g.: The oscillation of a bob of simple pendulum.<\/span><\/p>\n

                                            (ii)<\/span><\/em><\/strong>\u00a0<\/span><\/em><\/strong>\u00a0<\/span><\/em><\/strong>Damped Oscillation:<\/span><\/u><\/strong><\/p>\n

                                            If the amplitude of the oscillating particle changes w.r.t. time then oscillation of the particle is said to be damped oscillation, this occurs due to lose of energy of the oscillating particle due to friction of viscous mediums such as air, water etc.\u00a0<\/span>\u00a0<\/span>e.g: The oscillation of bob of pendulum in a fluid.<\/span><\/p>\n

                                            (iii)<\/span><\/em><\/strong>\u00a0<\/span><\/em><\/strong>\u00a0<\/span><\/em><\/strong>Maintained Oscillations:<\/span><\/u><\/strong>\u00a0<\/span><\/u><\/em><\/strong><\/p>\n

                                            If constant energy equal to lose of energy during oscillation of a body is supplied then damped oscillation becomes un-damped oscillation. Now the oscillation of the body under constant energy supply is called maintained oscillation.<\/span><\/p>\n

                                            20 Forced, Resonant and Coupled Oscillations:<\/span><\/u><\/strong><\/p>\n

                                            When a body oscillate under the effect of an external force then the oscillation of the body is called forced oscillation.<\/span><\/p>\n

                                            e.g.:- When the free hand of the simple pendulum is held by the hand and the pendulum is made to oscillate by giving Jerks by hand, then the oscillation of the pendulum is called forced oscillation.<\/span><\/p>\n

                                            Resonant Oscillation:<\/span><\/u><\/strong><\/p>\n

                                            If the frequency of driving force is equal to the natural frequency of the oscillator itself then the oscillation of the body is called resonant oscillation and the phenomenon is called resonance.e.g.:- Resonance causes disaster during earth quake i.e. when natural frequency of building become equal to earth quake then building damages.<\/span><\/p>\n

                                            Principal of Tuning of a radio receiver:<\/span><\/u><\/strong><\/p>\n

                                            We know that there are many signals of many stations around radio but we obtain a particular radio signal by setting a certain frequency of radio. When external frequency is same as that of stetted frequency then we listen that station.<\/span><\/p>\n

                                            Coupled Oscillation:<\/span><\/u><\/strong><\/p>\n

                                            A system of two or more oscillators linked together in such a way that there is a mutual exchange of energy between then, then the oscillation of the body is called coupled oscillations.\u00a0<\/span><\/p>\n

                                            E.g. Oscillations of loaded springs etc<\/span><\/p>\n

                                            \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                                            \u00a0<\/span><\/p>\n

                                            \u00a0<\/span><\/p>\n

                                            \u00a0<\/span><\/p>\n

                                            \u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

                                            Chapter 14 Oscillations class 11 physics notes To free download pdf of Chapter 14 Oscillations class 11 physics notes click on the link given below.. Chapter 14 Oscillations class 11 physics notes SANDEEP SONI\u2019S PHYSICS\u00a0COMPETITION CLASSES\u00a0\u00a0 (10+1, 10+2, IIT-JEE (Main & Advance),\u00a0NEET, B.Sc.\u00a0Agriculture,\u00a0NDA)\u00a0 OPP:\u00a0JHUNTHARA DHARAMSHALA\u00a0NEAR SURKHAB CHOWK,\u00a0HISSAR ROAD SIRSA\u00a0 \u00a0Unit-10: Oscillations and Waves\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0PH-\u00a094676-12340,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0Unit-10: Oscillations […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-2590","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"sandeep.soni484@gmail.com","author_link":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/author\/sandeep-soni484gmail-com\/"},"uagb_comment_info":0,"uagb_excerpt":"Chapter 14 Oscillations class 11 physics notes To free download pdf of Chapter 14 Oscillations class 11 physics notes click on the link given below.. Chapter 14 Oscillations class 11 physics notes SANDEEP SONI\u2019S PHYSICS\u00a0COMPETITION CLASSES\u00a0\u00a0 (10+1, 10+2, IIT-JEE (Main & Advance),\u00a0NEET, B.Sc.\u00a0Agriculture,\u00a0NDA)\u00a0 OPP:\u00a0JHUNTHARA DHARAMSHALA\u00a0NEAR SURKHAB CHOWK,\u00a0HISSAR ROAD SIRSA\u00a0 \u00a0Unit-10: Oscillations and Waves\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0PH-\u00a094676-12340,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0Unit-10: Oscillations…","_links":{"self":[{"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/pages\/2590","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/comments?post=2590"}],"version-history":[{"count":4,"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/pages\/2590\/revisions"}],"predecessor-version":[{"id":4641,"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/pages\/2590\/revisions\/4641"}],"wp:attachment":[{"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/media?parent=2590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}