Consider a vibrating system described by the initial value problem. (A computer algebra system is recommended.) u” + 1 4 u’ + 2u = 2 cos ωt

Question

Consider a vibrating system described by the initial value problem. (A computer algebra system is recommended.) u” + 1 4 u’ + 2u = 2 cos ωt, u(0) = 0, u'(0) = 2 (a) Determine the steady state part of the solution of this problem.

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5 months 2021-08-21T07:30:00+00:00 1 Answers 16 views 0

Therefore the required solution is

Explanation:

Given vibrating system is

Consider U(t) = A cosωt + B sinωt

Differentiating with respect to t

U'(t)= – A ω sinωt +B ω cos ωt

Again differentiating with respect to t

U”(t) =  – A ω² cosωt -B ω² sin ωt

Putting this in given equation

Equating the coefficient of sinωt and cos ωt

………(1)

and

……..(2)

Solving equation (1) and (2) by cross multiplication method

and

Therefore the required solution is