# Prove the lorentzian function describes resonant behavior

1. Sep 25, 2011

### Liquidxlax

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

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

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. Sep 27, 2011

### Liquidxlax

anyone got an idea? and something happend to my initial equations...

3. Sep 27, 2011

### vela

Staff Emeritus
You want to add a forcing term F(t) that drives the oscillator, so your equation becomes
$$m\ddot{x} = F(t) -kx -c\dot{x}$$Use something like F(t)=A sin ωt and find the particular solution to the differential equation.