5. A damped mass-spring system satisfies the differential equation and initial conditionsda+y+ 10x = F(t).dt2dt(a) When y = 0 and F(t) = 0, find the natural frequency of the system.(b) When F(t) = 0, find the values of y for which the system is over-damped, criticallydamped and under-damped.(c) When y = 6 and F(t) = 0, find the general solution x(t).(d) When y = 6 and F(t) = 25 cos 4t, use the method of undetermined coefficients to showthat a particular solution xp(t) isXp(t) =25cos 4t +10250sin 4t.51(e) What is the amplitude of æp(t)? HINT: use the method employed in question 3 of thisproblem set.

(a) The damped mass-spring system differential equation is given as : x''+γx'+10x=F(t) Putting γ=0…

Answered: 5. A damped mass-spring system…

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