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## Homework Statement

Derive the relationship bewteen x_{max}, A_{+}, A_{-} and \phi

## Homework Equations

x(t) = e^{\gamma t}(A_{+}e^{i \omega_d t} + A_{-}e^{-i \omega_d t})

x(t) = x_{max} e^{\gamma t} cos(\omega_d t + \phi)

## The Attempt at a Solution

I know the e^{\gamma t} cancels and for the imaginary parts to cancel, A_{+} = A_{-} but then i get x_{max}(cos(\omega_d t) cos(\phi) - sin(\omega_d t)sin(\phi)) = 2A_{+} cos(\omega_d) and i can't work out how to simplify it further