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JEE Main & Advanced Physics Simple Harmonic Motion Question Bank Displacement of S.H.M. and Phase

  • question_answer
    The periodic time of a body executing simple harmonic motion is 3 sec. After how much interval from time t = 0, its displacement will be half of its amplitude             [BHU 1998]

    A)            \[\frac{1}{8}\]sec               

    B)            \[\frac{1}{6}\]sec

    C)            \[\frac{1}{4}\]sec               

    D)            \[\frac{1}{3}\]sec

    Correct Answer: C

    Solution :

                       \[y=a\sin \frac{2\pi }{T}t\] Þ \[\frac{a}{2}=a\sin \frac{2\pi t}{3}\]Þ \[\frac{1}{2}=\sin \frac{2\pi t}{3}\]            Þ sin\[\frac{2\pi t}{3}=\sin \frac{\pi }{6}\] Þ \[\frac{2\pi t}{3}=\frac{\pi }{6}\] Þ \[t=\frac{1}{4}\sec \]


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