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

  • question_answer
    The time period of a simple pendulum is 2 sec and its amplitude is 10 degree. Its amplitude decreases to 5degree after 10 oscillations. The ?relaxation time? (in sec.) will be :

    A)  \[20.76\]                                            

    B)  \[34.76\]

    C)  \[15.46\]                                            

    D)  \[28.6\]

    Correct Answer: D

    Solution :

    The time in which amplitude decreased to 1/e to its original value of the damped oscillation is called relaxation time \[(\tau )\] \[\tau \,=1/b\] where b is damping factor in unit per second             \[A={{A}_{0}}{{e}^{-bt}}\]             \[5={{10}_{e}}^{-b\,20}\] \[\tau =1/b=20/\ln \]           \[\tau =\,\frac{20}{693}\,=28.6\]


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