# Oscillations: Amplitude and Energy Reduction

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.

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