4. 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.
4. 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.
5. a. Find the solution of the initial value problem in Problem 4.
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.
I understand 4 but need help with 5
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