Amplitude Ratio

  • Thread starter bclark23
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In the figure below, a damped simple harmonic oscillator has mass m = 300 g, k = 95 N/m, and b = 70 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)?

I know I need to find the period (T), which is 2πsqrt(m/k).
T=2πsqrt[(.0kg)/(95nN/m)]=.353 s

Also, there are 20 cycles, so the final time would be (20 cycles)(.353s)=7.062s

The formula for damping (Adamped?) is x(t)=xme-bt/2mcos(wt+rho)
The formula for oscillation (Ainital?) is x(t)=xmcos(wt+rho)

I'm pretty sure I need to use these two equations, and put the answers in a ratio, but I'm not sure how to go about doing that.
 

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  • #2
haruspex
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The formula for damping (Adamped?) is x(t)=xme-bt/2mcos(wt+rho)
Don't you just substitute for b, t and m in e-bt/2m to find the attenuation?
 
  • #3
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Yes, that was exactly it! Thank you
 

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