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**Solving differential with a step impulse.**

Hi,

I have problem I know I should be able to do but I've been stuck on it for a while. Just looking to be pointed in the right direction.

(dq^2/d^2t) + 2*ζ*ω*dq/dt + (ω^2)*q = u(t)/L

Where u(t) is a step impulse, q is the charge through an inductor. So q and dq/dt (the current) are both = 0 at t = 0.

So I have to solve q(t) for the damping constant ζ <1, >1 and =0.

I tried getting the laplace of it and then getting Q(t) on one side but solving the inverse laplace of the result from tables is impossible and I'm not sure that's how this is supposed to be solved as I've seen many different solutions to similar problems.

Is Laplace the right thing to do? And if so what am I missing to solve it.

If not Laplace then what? Should I be plugging in an e^-st for q or something?

Thanks any help is appreciated.