# Are all damped oscillations periodic?

1. Oct 26, 2015

### Himanshu_6174

I know the equation for damped oscillation where the damping force depends on velocity. In that case the damped oscillation has a fixed angular frequency and thus time period! I am wondering if there are any types of damped oscillation where the time period is not constant i.e. the motion is not periodic!

2. Oct 26, 2015

### Krylov

For a free (i.e. non-driven) damped harmonic oscillator in the strongly damped or critically damped regime, the motion is not periodic. It's only periodic in the weakly damped regime.

If you consider a pair of undamped harmonic oscillators, then their phase space dynamics on the torus may display quasi-periodic (but not periodic) motion depending on the (ir)rationality of the ratio of their frequencies. This is probably the simplest example of non-periodic motion.

Last edited: Oct 26, 2015