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: Damped Driven Oscillator

  1. Sep 8, 2009 #1
    1. The problem statement, all variables and given/known data
    A driven oscillator with mass m, spring constant k, and damping coefficient b is is driven by a
    force [tex]F_{o}cos(\omega t)[/tex]. The resulting steady-state oscillations are described by [tex]x(t) = Re{\underline{A}e^{i\omega t}}[/tex] where:

    [tex]\underline{A} = \frac{F_{0}/m}{(\omega_{o}^{2} - \omega^{2}) + i(2\omega/\tau)} = Ae^{i\varphi} , \omega_{o} = \sqrt{k/m} , \tau \equiv 2m/b [/tex]

    Show that for light damping ([tex]Q = \tau \omega_{o} / 2 >> 1[/tex]), the maximum amplitude occurs at approximately [tex]\omega = \omega_{o}[/tex] and that the maximum amplitude is approximately Q times the amplitude for very low driving frequencies.

    2. Relevant equations

    3. The attempt at a solution
    The amplitude is [tex]Ae^{i\varphi}[/tex] which has its maximum magnitude when [tex]\varphi = -\pi/2[/tex]. Therefore, the driving frequency must be near the resonant frequency so that the term is completely imaginary and negative, creating a phase angle of -90 degrees. I don't understand what the light damping and quality factor has to do with this, however, nor how to prove the value of the amplitude. The amplitude for low driving frequencies is [tex]\frac{F_{0}/m}{\omega_{o}^{2}}[/tex].....
    Last edited: Sep 8, 2009
  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