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JEE Main & Advanced Sample Paper JEE Main Sample Paper-35

  • question_answer
    The displacement y of a particle executing periodic motion is given by:\[y=4{{\cos }^{2}}\left( \frac{1}{2}t \right)\sin 1000\,t)\] How many independent harmonic motions may be considered to be a result of the superposition by this expression?

    A)  six                                         

    B)  five

    C)  four                                     

    D)  three

    Correct Answer: D

    Solution :

    The given equation is:             \[y=2(2{{\cos }^{2}}t/2)\,\sin (1000)t\]             \[=2(1+\cos t)\sin (1000)t\]             \[=2\cos t\sin (1000)\,t+2\sin (1000)t\]             \[=\sin (1001)\,t+\sin (999)\,t+2\sin (1000)t\] Thus 3 independent harmonic motions superimpose.


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