A mechanical system is often acted on by an external force or large magnitude that acts only for a very short period of time, like a hammer blow, explosion, or lightning strike. The Dirac Delta function o(f-a) (also known as the unit impulse function) is used to model such a force at time . It is commonly regarded as a spike of indeterminate magnitude at time r = a whose integral over the real numbers is equal to one. Solve y"+ y=46(1-24), y(0)=1, v'(0)=0. This could model the motion of a mass on a spring, no damping, with the mass released from rest one unit below the equilibrium position. At time , the mass is given a sharp blow by a hammer strike. Extra Credit 8 pts x'=3y-6 Consider the nonlinear planar system y'=3x-x2