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**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.

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?**