(adsbygoogle = window.adsbygoogle || []).push({}); Question: A damped harmonic oscillator loses 5.0 percent of its mechanical energy per cycle.(a)By what percentage does its frequency differ from the natural frequency [itex]\omega_0 = \sqrt{k/m}[/itex]?(b)After how may periods will the amplitude have decreased to 1/e of its original value?

So, for (a), the answer is [itex]\omega ' / \omega_0[/itex] where

[tex]\omega ' = \sqrt{\frac{k}{m} - \frac{b^2}{4m^2}}[/tex]

But that leaves me with 3 unknowns, k, m, and b requiring three equations to solve. The only equations I can think of is E = K + U (mechanical energy) and E = 0.95^{T}E_{0}where T is the number of cycles and E_{0}is the initial mechanical energy.

What other equation can I use? Or is there a simpler method of finding the solution?

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# Damped Harmonic Oscillator & Mechanical Energy

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