A mass-spring system with shock absorber consists of a mass of 50 kg fixed at

a spring with a return constant of 250 N/m and a damping constant of 100 N * second/m.

a)It is assumed that no external force is exerted on the mass and that the

initial conditions on position and speed are not null. Determine if

the system described above is a case of under-depreciation, depreciation

critical or over-amortization. Justify.

b) If we assume that the initial conditions are null and that an external force

of the form f(t) = 50 (t-3) exerts itself on the mass, determine the position of it as a function of time

c) If the external force is given by f(t)=50 cos(2t), find the period and

the amplitude of the solution in steady state.