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.

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

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement

overcharge is the right answer system