So we have derived that for the differential equation:(adsbygoogle = window.adsbygoogle || []).push({});

##x(t)''+x(t)=\delta(t)##

The solution is given by ##x=sin(t)H(t)## where ##H## is the Heaviside function.

To find this we assumed that the system was in rest before ##t=0## and that position and velocity are continious.

QUESTION: I am pretty sure that this ##sin(t)H(t)## is just a particular solution, is it correct to say that if one doesn't assume that the system in rest the general solution is given by ##x=Acos(t)+Bsin(t)+H(t)sin(t)##? So basically, is the solution we found in class a particular solution and thus can I always add a homogeneous solution to it?

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# Green's function for SHO

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