For u"+2u'+6u=15cos(3t), find the steady-state solution and identify its amplitude and phase shift.

u=A cos 3t+B sin 3t

15 cos 3t= -9A cos 3t-9B sin 3t+2(-3A sin 3t+3B cos 3t)+6(A cos 3t+B sin 3t)

= -9A cos 3t-9B sin 3t-6A sin 3t+6B cos 3t+6A cos 3t+6B sin 3t

= -3A cos 3t-3B sin 3t-6A sin 3t+6B cos 3t

=A cos 3t+B sin 3t+2A sin 3t-2B cos 3t

Now what? Help me step by step.

## Comments

Can you tell me how to find the phase shift? The answer should be ˜-0.464.