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JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Oscillations

  • question_answer
    A pendulum with time period of 1s is losing energy. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in s~1) is :

    A) \[\frac{1}{2}\]

    B) \[\frac{1}{30}\]

    C) 2

    D) \[\frac{1}{15}In\,3\]

    Correct Answer: D

    Solution :

    [d] As we know, \[E={{E}_{0}}{{e}^{-\frac{bt}{m}}}\] \[15=45{{e}^{-\frac{b15}{m}}}\Rightarrow \frac{1}{3}={{e}^{-\frac{b15}{m}}}\] [As no. of oscillations = 15 so t = 15 sec] Taking log on both sides \[\frac{b}{m}=\frac{1}{15}ln\,\,3\]


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