I am so lost on Green's functions... plz help me...

3. Green's functions. Find an explicit expression for the Green's function G(t, t') for the critically damped harmonic oscillator. By construction the Green's func tion must satisfy the conditions G(t, t) = O and (1065, t) = 1. Check that your result satises these conditions. Use your result to solve the problem 51% + 2351\" + 2a: = t) with $05) = :i:(t) = 0 for t 0, and (b) f(t) = 0, t 0. Derive the result (b) by an alternative and more direct method