JEE Main & Advanced Physics Simple Harmonic Motion JEE PYQ-Simple Harmonic Motion

  • question_answer
    A block of mass 0.1 kg is connected to an elastic spring of spring constant \[640\,\,N{{m}^{-1}}\] and oscillates in a damping medium of damping constant \[{{10}^{-2}}kg\,{{s}^{-1}}\]. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to [JEE Online 09-04-2017]

    A)  2 s                  

    B)       5 s

    C)  7 s                  

    D)       3.5 s

    Correct Answer: D

    Solution :

    [d] \[E'=\frac{1}{2}\]\[b=\frac{\lambda }{m}\] \[A={{A}_{0}}{{e}^{-bt}}\]
    \[a'=\frac{a}{\sqrt{2}}\] \[\lambda =bm\] \[\frac{1}{\sqrt{2}}\,={{e}^{-\frac{t}{10}}}\]
    \[b=\frac{1}{10}\,\sqrt{2}\,={{e}^{\frac{1}{10}}}\]
    \[\ln \,\sqrt{2}\,=\frac{t}{20}\]


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