How Does Friction Affect the Amplitude of a Harmonic Oscillator Over Time?

[belleamie]

Please help
1) The mechanism which powers the clock (using a harmonic oscillator to keep time with friction) Since the clock has friction the oscillation amplitude decreases in time. If the oscillation amp is unity at t=0 what will the amp be after 10 sec?

I believe we need to use the equation w=sq rt(k/m-(c/2m)^2)
But I'm not exactly sure what is the correct way to arrpoach this problem, Any hint would be appreciated! thanks!

 

[lightgrav]

They're not asking (at this point) for the new *angular frequency*,
they're asking for the *envelope* of the decaying cosine curve.
x(t) will be A_o exp(-t/tau) cos(wt + phi) ; the question is about
the exp(-t/tau) portion. You need to know how strong friction is,
or how much frictional work is done in a cycle with total Energy E.