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Amplitude Ratio

  1. Nov 14, 2012 #1
    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.
     
  2. jcsd
  3. Nov 14, 2012 #2

    haruspex

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    Don't you just substitute for b, t and m in e-bt/2m to find the attenuation?
     
  4. Nov 14, 2012 #3
    Yes, that was exactly it! Thank you
     
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