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JEE Main & Advanced Physics Simple Harmonic Motion Question Bank Critical Thinking

  • question_answer
    The displacement y of a particle executing periodic motion is given by\[y=4{{\cos }^{2}}(t/2)\sin (1000t)\]. This expression may be considered to be a result of the superposition of........... independent harmonic motions                          [IIT 1992]

    A)            Two                                         

    B)            Three

    C)            Four                                         

    D)            Five

    Correct Answer: B

    Solution :

                       \[y=4{{\cos }^{2}}\left( \frac{t}{2} \right)\sin 1000\ t\]                    \[\Rightarrow y=2(1+\cos t)\sin 1000\ t\]                    \[\Rightarrow y=2\sin 1000\ t+2\cos t\ \sin 1000t\]                    \[\Rightarrow y=2\sin 1000\ t+\sin 999\ t+\sin 1001\ t\]            It is a sum of three S.H.M.


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