{"id":3594,"date":"2022-01-15T02:50:13","date_gmt":"2022-01-15T02:50:13","guid":{"rendered":"https:\/\/physics.educour.in\/isc-physics\/?p=3594"},"modified":"2023-12-24T16:30:32","modified_gmt":"2023-12-24T16:30:32","slug":"simple-harmonic-motion","status":"publish","type":"post","link":"https:\/\/physics.educour.in\/isc-physics\/simple-harmonic-motion\/","title":{"rendered":"SIMPLE HARMONIC MOTION"},"content":{"rendered":"\t\t
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Contents<\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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  1. Periodic Motion<\/a><\/li>
  2. Oscillatory Motion<\/a><\/li>
  3. Simple Harmonic Oscillation<\/a><\/li>
  4. SHM and uniform circular motion<\/a><\/li>
  5. Characteristics of SHM<\/a><\/li>
  6. Energy in SHM<\/a><\/li>
  7. Simple Pendulum<\/a><\/li>
  8. Spring Mass System<\/a><\/li>
  9. Additional Examples of SHM<\/a><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    Periodic Motion:<\/u><\/span><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    \u00a0(i) When a body moves on a definite path and repeats its motion again and again after a definite interval of time, then its motion is called periodic motion.\u00a0<\/span><\/p>

    The constant time interval after which it repeats its motion called its time period of motion, T.<\/strong><\/span><\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Example :<\/strong> Motion of earth around Sun ( T=365.25 days), Motion of minutes hand in clock (T= 1hour), Motio of a simple pendulum in free space, etc.<\/span><\/p>

    So, for motion of a body to be periodic,<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 * Body must move on a definite path.<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 * It must repeat its motion after a definite time interval.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Oscilatory Motion:<\/u><\/span><\/h3>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    When a body makes to and fro motion about a fixed point, on a almost straight line path and repeats its motion after a definite time interval, then the motion of the body is a vibratory motion or oscillatory motion<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 * It must have periodic motion<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 * The body must move to & fro about a fixed point on a almost straight line\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0path.<\/span><\/p>

    The point about which the body makes to and fro motion is called its mean position.\u00a0<\/strong><\/span><\/span><\/p>

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>Example: <\/strong>\u00a0<\/span><\/p>

    (i) Motion of a bob of a simple pendulum if displacement is small, (ii) Motion of a mass attached to a spring,<\/span><\/p>

    (iii) Motion of a block, moving with constant speed, on a smooth horizontal floor between two rigid walls.<\/span><\/p>

    * Every oscillatory motion must be a periodic motion but every periodic motion is not oscillatory.<\/span><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Go to Table of Contents\u2192<\/strong><\/span><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Simple Harmonic Motion<\/u><\/span><\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    When a body makes oscillatory motion about a fixed mean position such that the acceleration of the body at any instant is directly proportional to its displacement from the mean position & is always directed towards the mean position<\/em><\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 a\u00a0 \u221d\u00a0 \u2013x<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 or\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 a\u00a0 =\u00a0 \u2013 \u03c92 <\/sup>x\u00a0\u00a0\u00a0\u00a0\u00a0 \u2026\u2026\u2026\u2026\u2026\u2026.. (1)<\/span><\/p>

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Where,\u00a0 \u03c9 (const)\u00a0 =\u00a0 angular frequency<\/span><\/p>

    According to Newtons second law \u2013<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 F =\u00a0 ma<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 or\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 F = \u2013m\u03c92<\/sup>x<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 F = \u2013k x\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u2026\u2026\u2026\u2026\u2026\u2026.. (2)<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 i.e.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 F \u00a0\u00a0\u00a0\u00a0 \u221d\u00a0 \u2013x<\/span><\/p>

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Where,\u00a0 k = Force constant<\/span><\/p>

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Since, the force is always directed towards the mean position it is called restoring force.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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