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NEET Physics Simple Harmonic Motion NEET PYQ-Simple Harmonic Motion

  • question_answer
    The displacement of a particle along the x axis is given by \[x=a{{\sin }^{2}}\omega t\]. The motion of the particle corresponds to                                                                                                                         [AIPMT (S) 2010]

    A)  simple harmonic motion of frequency \[\omega /\pi \]

    B)  simple harmonic motion of frequency \[3\omega /2\pi \]

    C)  non simple harmonic motion

    D)  simple harmonic motion of frequency \[\omega /2\pi \]

    Correct Answer: C

    Solution :

    For a particle executing SHM acceleration  \[\propto -{{\omega }^{2}}\] displacement (x)                              ... (i)
    Given    \[x=a{{\sin }^{2}}\omega t\]                            ...(ii)
    Differentiating the above equation w.r.t, we get
    \[\frac{dx}{dt}=2a\omega (\sin \omega t)(\cos \omega t)\]
    Again differentiating, we get
    \[\frac{{{d}^{2}}x}{d{{t}^{2}}}=a=2a{{\omega }^{2}}[{{\cos }^{2}}\omega t-{{\sin }^{2}}\omega t]\]
    \[=2a{{\omega }^{2}}{{\cos }^{2}}\omega t\]
    The given equation does not satisfy the condition for SHM [Eq. (i)]. Therefore, motion is not simple harmonic.


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