- #1

vanceEE

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## Homework Statement

$$ M \frac{d^2x}{dt^2} + c\frac{dx}{dt} + kx = F_{0}cos \omega t $$

## The Attempt at a Solution

$$x(t) = asin\omega t + bcos \omega t $$

$$ a = \frac{\omega c F_{0}}{(k-\omega^2M)^2 + \omega^2c^2} $$

$$ b = \frac{(k-\omega^2M)F_{0}}{(k-\omega^2M)^2 + \omega^2c^2} $$

$$ x_{0}(t) = \frac{F_{0}}{(k-\omega^2M)^2 + \omega^2c^2} [\omega c sin \omega t + (k-\omega^2M)cos \omega t] $$

How can I use arctan to write this particular solution in a more useful form?