- #1
shyta
- 56
- 0
Homework Statement
Consider critically damped harmonic oscillator, driven by a force F(t)
Find the green's function G(t,t') such that x(t) = ∫ dt' G(t,t')F(t') from 0 to T solves the equation of motion with x(0) =0 and x(T) =0
Homework Equations
x(t) = ∫ dt' G(t,t')F(t') from 0 to T
The Attempt at a Solution
Hi guys, I am completely new to green's function.. need a lot of help understanding the use, and how to use it >_<
I've been doing some readings and this is what i understand so far
x = [itex]x _{h}[/itex] + ∫G(t,t')f(t') dt'
i.e. G(t,t') will be the particular solution to the ode with F(t) = δ(t-t')
does this mean that I should let [itex]\ddot{x}[/itex] +2γ[itex]\dot{x}[/itex] + [itex]ω _{0}[/itex]² = δ(t-t') and solve this to get the green's function?