1 ) a 1kg mass oscillates on a spring with spring constant K=1. The mass starts 2 meters above equilibrium with an initial velocity of 2 meters per second downwards direction and begins its free motion. After one full oscillation it is hit with a hammer with an impulse force that has an unknown magnitude of F0 Newtonsa) Write down the differential equation completely, including the RHS in terms of F0 and the correct delta function and the ICS. Treat the upwards direction as positive.

b) Determine the motion. Express solution fully simplified piecewise function (still depend on F0)

c) Determine the final amplitude of oscillation as a function of the unknown magnitude F0d)   Use mathematics and clear mathematical reasoning that it is impossible for the hammer blow to stop the motion completely (hint: what does amplitude have to be for there to be no more motion?)

e) Explain the physics behind what you showed in part c (ie: why this hammer hit can not stop it)

f) Determine the magnitude F0 & direction of the hammer hit that minimizes the amplitude and determine the min amplitude