Answer:
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
