A mass of 1 kg stretches a spring (9.8/625) m. The mass is acted on by an external force of 100cos(10t) and moves in a medium that imparts a viscous form of 40 N when the speed of the mass is 1 m/sec. The mass is set in motion from its equilibrium position with a velocity of 0 m/sec.

a.) Formulate the initial value problem describing the motion of the mass.

b.) Solve.

Determine a suitable form for Y(t), a solution to the 2nd order linear non-homogeneous differential equation y'' + 40 y' + 625 y = 10 cos(15t)