Prove the lorentzian function describes resonant behavior

[Liquidxlax]

Homework Statement

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

Homework Equations

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

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

 

[Liquidxlax]

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

 

[vela]

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.