Deriving the response amplitude

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For the system:
$z''(t)-\delta z'(t)+\kappa^2z(t)=Asin(wt)$
How can you derive the response amplitude $R$?
(I have figured out that the solution is of the form $z_p(t)= Rsin(wt+\psi)$, however I am unsure of how to cancel out the trigonometric terms)