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  3. *please show all work* consider a damped, forced m

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

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Advance Math

*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 themass at time t, with x = 0 corresponding to the equilibriumposition. Suppose the mass m = 1 kg, the damping constant c = 3N·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 theposition function x(t).

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

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