1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Amplitude Ratio Date
B Composition of Light Feb 14, 2018
B Pitch and amplitude of sound wave Vs its volume Feb 4, 2018
B Rocket Mass Ratio Query Dec 8, 2017
I Refraction Convergence and Amplitude change- Ocean waves Oct 30, 2017