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## Homework Statement

I need to find the forced response of a mass-spring-damper system by using Laplace Transform.

## Homework Equations

Equation of motion:

[tex] \ddot{x} + 2 \zeta \omega_n \dot{x} + {\omega_n}^2 x = \frac{F}{m} cos \left( \omega t \right) [/tex]

## The Attempt at a Solution

At the Laplace domain, we have:

[tex] X \left( S \right) = \frac{F/m}{S^2+ 2 \zeta \omega_n S + {\omega_n}^2} \frac{S}{S^2+\omega^2} [/tex]

After this point, I try to make partial fractions, but I must be missing something. It results in a page full of algebra, and it does not look like the correct solution.

Please, could you help me on figuring out what I should do?

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