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    Oscillations: Amplitude and Energy Reduction

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    An oscillator with a mass of 420g and a period of 0.800s has an amplitude that decreases by 2.30% during each complete oscillation.

    A) If the initial amplitude is 7.00cm, what will be the amplitude after 31.0 oscillations?

    B) At what time will the energy be reduced to 65.0% of its initial value?

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    Solution Preview

    After a the first period the amplitude will be A(1) = A(0)*0.977
    After the second period the amplitude will be A(2) = A(1)*0.977 = A(0)*0.977^2
    It is easy to see that after N periods, the amplitude will be A(N) = A(1)*0.977^N

    In our case, N=31 and A(0)=7cm

    Thus, after 31 ...

    Solution Summary

    This solution solves for an oscillator's amplitude and the time that its energy will be reduced to 65% of its initial value.