Solve the initial value problem

x''+16x=9cos(2t), x(0)=2 x'(0)=2
(where primes indicate derivatives with respect to t). Express your solution as the sum of two oscillations,
x(t) = cos( _____t -_____ ) +_____ cos(_____ t )
(Recall that alpha must be between 0 and 2.)

Question

Solve the initial value problem

x''+16x=9cos(2t),  x(0)=2  x'(0)=2
(where primes indicate derivatives with respect to t). Express your solution as the sum of two oscillations,
x(t) =   cos( _____t -_____  ) +_____  cos(_____ t ) 
(Recall that alpha must be between 0 and 2.)

anonymous · Answer

Annihilators would work here. And then after annihilating it, taking the auxiliary equation should help.