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JEE Main & Advanced Sample Paper JEE Main Sample Paper-24

  • question_answer
    The displacement y of a particle is given by, \[y=4{{\cos }^{2}}\left( \frac{1}{2} \right)\sin (1000\,\,t)\]. This expression may be considered to be a result of the superposition of how many simple harmonic motions?

    A)  2                                

    B)  3

    C)  1                                

    D)  none

    Correct Answer: B

    Solution :

    Given \[y=4{{\cos }^{2}}\left( \frac{t}{2} \right)\,\sin (1000t)\] \[=2(1+\cos t)\,\sin (1000t)\] \[(\therefore \,\,1+\cos \theta f\,=2{{\cos }^{2}}\,\frac{\theta }{2})\] \[=2\,\sin 1000\,t+2\,\cos t\sin \,1000\,t\] \[=2\,\sin 1000t+\sin (1001)\,t+\sin (999)t\] Therefore, it consists of 3 SHM?s


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