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  3. consider a damped forced mass-spring system with m

Consider a damped forced mass-spring system with m = 1, γ = 2, and k =...

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Advance Math

Consider a damped forced mass-spring system with m = 1, γ = 2,and k = 26, under the influence of an external force F(t) = 82cos(4t).

a) (8 points) Find the position u(t) of the mass at any time t,if u(0) = 6 and u 0 (0) = 0

. b) (4 points) Find the transient solution uc(t) and the steadystate solution U(t). How would you characterize these two solutionsin terms of their behavior in time?

c) (4 points) Find the amplitude R and the phase angle δ forthis motion and express U(t) as a single trigonometric term: U(t) =R cos(ωt − δ).

d) (4 points) Justify the following description of what happens:“the transient motion uc(t) dies out with the passage of time,leaving only the steady state periodic motion U(t)

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