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I am trying to understand how the Green's functions work, and how to come up with one for a given differential equation. Now, I need to write down the Green's function for 3 different types of differential equations. They are simply, underdamped, critically damped, and overdamped oscillators. I know that the Green's functions are easy to come up with for above mentioned cases if you know the homogenous solution (just replace t with (t - t')), but I am not exactly sure how the heavyside (step-function) gets involved with this. Moreover, I know that the Dirac-delta function is very useful in solving the nasty integrals, but I dont really understand how we are using them. I basically need help in coming up with Green's functions for 3 different kinds of oscillators. Any help on the step-function and the impulse function (as forcing functions), would also be greatly appreciated. Thanks in advance for any help.

- harsh

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# Difficulties understanding Green's Functions

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