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A mass of 5 kg stretches a spring 10 cm. the mass is acted on by an external force of 10sin(t/2) N (newtons) and moves in a medium that imparts a viscous force of 2 N when the speed of the mass 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 most ion of the mass.

a) find the solution of the initial value problem
b) identify the transient and steady state parts of the solution
c) plot the graph and the steady state solution
d) if the given external source is replaced by a force of 2 cos wt of frequency w, find the value of w for which the amplitude of the force response is maximum.

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