# Driven Harmonic Oscilator

1. Driven Harmonic Oscillator with an arbitrary driving force:
f(t)=x"+2bx'+w^2 x
Let x(t) be expressed by x(t)= g(t)*exp(a1*t), where a1 is a solution to the characteristic equation a^2 + 2ba+w=0 for the above second order differential equation. Find the ordinary differential equation that is satisfied by G. There's more parts, but im jsut really stuck at the first part.

3.I'm not even really sure where to start. Im thinking i have to differentiate x(t) to get x'(t) and x"(t). then i plug that back into the original differential. is that correct?