1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Damped harmonic motion

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    A damped harmonic oscillator has mass m , spring constant k , damping force
    - cv .

    (a) Find the ratio of two successive maxima of the oscillations.

    (b) If the oscillator has Q = 100 , how many periods will it take for the amplitude to decay to 1/ e
    of it’s initial value? What fraction of the initial energy the oscillator has left by this time?

    2. Relevant equations

    3. The attempt at a solution

    Okay, so for a)

    T_d=2pi/omega_d = 2pi/(omega_0^2 - gamma^2)

    The ratio is equal to e^-(gamma * T_d)

    so r = e^-(c/2m * 2pi/(k/m - (c/2m)^2)^1/2)

    But then for b, I'm lost again.

    If Q = 100, omega_d=200*gamma.

    So the ratio of successive maxima = e ^ - pi/100

    But i'm not sure how that lets me figure out how many periods will it take for the amplitude to decay to 1/ e of it’s initial value.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Damped harmonic motion Date
Lyapunov exponents of a damped, driven harmonic oscillator May 6, 2016
Damped Harmonic Oscillator Dec 11, 2013
Simple Harmonic Oscillator and Damping Nov 16, 2013
Damped Harmonic motion Apr 23, 2009
Damped Simple Harmonic Motion Oct 27, 2005