- #1
dacruick
- 1,042
- 1
Hi there,
I just started an intermediate classical mechanics course at university and was smacked upside the head with this question that I don't know how to even start.
We are to find the response function of a damped harmonic oscillator given a Forcing function. The forcing function for t>0 is
F(t) = F(0)exp(-λt)*sin(wt)
where λ is a constant, F(0) is the initial force, w is the angular frequency, and t is time.
The equation of motion of a damped harmonic oscillator which I believe to be
x'' + 2bx' + wo2x = F(t)
I haven't really even attempted this solution. I've been looking online for a direction, and I saw one example that told me to guess a particular solution based on the forcing functions proportionality to eiwt. It doesn't tell me why I should be doing that, and to be honest, I don't even really understand what Greens theorem is.
Any help would be very greatly appreciated,
Thanks!
I just started an intermediate classical mechanics course at university and was smacked upside the head with this question that I don't know how to even start.
Homework Statement
We are to find the response function of a damped harmonic oscillator given a Forcing function. The forcing function for t>0 is
F(t) = F(0)exp(-λt)*sin(wt)
where λ is a constant, F(0) is the initial force, w is the angular frequency, and t is time.
Homework Equations
The equation of motion of a damped harmonic oscillator which I believe to be
x'' + 2bx' + wo2x = F(t)
The Attempt at a Solution
I haven't really even attempted this solution. I've been looking online for a direction, and I saw one example that told me to guess a particular solution based on the forcing functions proportionality to eiwt. It doesn't tell me why I should be doing that, and to be honest, I don't even really understand what Greens theorem is.
Any help would be very greatly appreciated,
Thanks!