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3. A mass of 5 kg stretches a spring 10 cm. The mass is acted on...

3. A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10 sin(t/2) N (newtons) and moves in a medium that imparts a viscous force of 2 N when the speed of the mass is 4 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/s, formulate the initial value problem describing the motion of the mass. Then (a) Find the general solution (b) Identify the transient and steady state parts of the solution. (c) Plot the graph of the steady state solution. (d) If the given external force is replaced by a force of 2 cos ωt of frequency ω, find the value of ω for which the amplitude of the forced response is maximum. please show all work and explain

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