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