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!

Homework Help: Question Involving Damped Harmonic Oscillators and Periods

  1. Sep 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Given: The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of period of the oscillation to the period of the same oscillator with no damping is given by

    T(sub d)/T(sub o) = (1 + (1/4([tex]\pi[/tex]^2)(n^2)))^1/2

    2. Relevant equations

    T(sub d) = (2[tex]\pi[/tex])/[tex]\omega[/tex][tex]_{d}[/tex]

    T(sub o) = (2[tex]\pi[/tex])/((k/m)^1/2)

    A/A(sub o) = 1/2 = e^(-t/2[tex]\tau[/tex])

    n = [tex]\omega[/tex][tex]_{d}[/tex]t/2[tex]\pi[/tex]

    3. The attempt at a solution

    I have tried dividing T(sub d) by T(sub o) to find a solution, and subbing known variables into the A/A(sub o) and n equations, to no avail. I have looked ahead to the solution to try to find a way to work towards it, but I don't know where I should start in order to go in the right direction.

    Please help!
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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