# SAGE : Solving Second Order Non-Homogeneous Differential Equations

## Mechanical Vibrations with an External Forcing Function

Solve the equation: $4u''(t)+4u'(t)+17u=20\cos(6t)$ with $u(0)=2$ and $u'(0)=0$.

- First plot the transient solution, or $y_h$

Next we can plot the external forcing function (scaled down by 15)

What will the steady-state solution looke like? Think about pulling a pushing to natural trnsient state with the periodic forcing function.