Consider an unforced harmonic oscillator with frequency ?? which satisfies the equation

yn+w2y=0.

Suppose the mass is struck once with a hammer force of 4 units at time t=8, and the mass was initially displaced 3 units (positive downwards) and let go with 2 units of initial velocity. Set up the initial value problem corresponding to this situation, where the hammer strike is modeled by a Dirac delta generalized function

F=Kb(t-c)

and initial conditions

y(0)=y0, y`(0)=y1.

Find the parameters K, c, y0 and y1.