Problem 3: [8P] Use the method of Green's functions to solve the following initial value problem describing the motion of a mass-spring system: dy +36ysin 6t dt y(0) = 0 dy 1 (0) = dt 12 where y(t) represents the displacement of the system at time t. Does the system undergo resonance? Justify your answer. Hint: sin A sin B cos A cos B = - cos(A B) cos(A + B) - 2 cos(A B) + cos(A + B) - 2 sin(AB)=sin A cos B + cos A sin B cos(AB) = cos A cos B + sin A sin B