Energy in Simple Harmonic Motion Video Lessons

Concept

# Problem: The amplitude of a lightly damped harmonic oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?

###### FREE Expert Solution

The mechanical energy of a simple harmonic oscillator:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{A}}}^{{\mathbf{2}}}}$

E0 = 0.5k(A0)2

A1 = [A0 - (3/100)A0] = 0.97A0

E1 = (1/2)k•(A1)2 = (1/2)k•(0.97A0)2 = 0.47045k(A0)2

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###### Problem Details

The amplitude of a lightly damped harmonic oscillator decreases by 3.0% during each cycle.

What percentage of the mechanical energy of the oscillator is lost in each cycle?