Pendulum with Dirac Comb excitation
where l, b, g, G are constants and .
Show that the resulting motion is given by
[terms with frequencies ]
and explain why the higher frequency terms are supressed.
My first take was to rearrange to
Then, taking the Laplace transform of both sides I got
which, as far as I'm concerned transforms to
And, assuming that this is a correct form of the solution, I can't see how that is equivalent with the function given in the question. I reckon it has something to do with using Fourier series/transform instead? If so, I'm not sure how to do that. Or, is there a way to convert my solution into the given one?
I've been struggling with this for a good few days now, so any help would be much appreciated.