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: Prove the lorentzian function describes resonant behavior

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data

    Resonances occur in many physical systems, and are often observed by measuring the frequency response of the system to an applied driving force. use the example of a damped harmonic oscillator to show how the lorentzian function serves as a good description of resonant behavior

    2. Relevant equations

    [itex]P_{L}( x; \mu ,\Gamma)[/itex] = [itex]\frac{\Gamma/2}{\pi(x-\mu)^{2} +( \Gamma/2)^{2} }[/itex]


    3. The attempt at a solution

    this is for an honours lab, and the "lecture" part isn't taught well at all. So i kind of need help to start this problem
  2. jcsd
  3. Sep 27, 2011 #2
    anyone got an idea? and something happend to my initial equations...
  4. Sep 27, 2011 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You want to add a forcing term F(t) that drives the oscillator, so your equation becomes
    [tex]m\ddot{x} = F(t) -kx -c\dot{x}[/tex]Use something like F(t)=A sin ωt and find the particular solution to the differential equation.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook