Question

In: Advanced Math

*PLEASE SHOW ALL WORK* Consider a damped, forced mass/spring system. Let t denote time (in seconds)...

*PLEASE SHOW ALL WORK*

Consider a damped, forced mass/spring system. Let t denote time (in seconds) and let x(t) denote the position (in meters) of the mass at time t, with x = 0 corresponding to the equilibrium position. Suppose the mass m = 1 kg, the damping constant c = 3 N·s/m, the spring constant k = 2 N/m, the external force is F (t) = 20 cos(2t), the initial position

x(0) = 1 m, and the initial velocity x′(0) = 2 m/s. a. Find the position function x(t).

b. What part of the solution is the transient part and what part is the steady-state part?

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Expert Solution

Colby Messinger answered 1 year ago
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