# Damping/decay rate

1. Nov 8, 2011

### tommo123

I've got data that's force (g) against time for an SDOF system (with a bit of noise). The main thing I'm interested in is calculating the damping parameters, where it's exponential decay (is that called viscous?).

I've calculated the exponential envelope in Matlab, which gives me a nice exponential curve. How would I then get the damping coefficient from this, and what would my units be? Alternatively I could work from a logarithmic graph and fit a line (of the form y=mx+c), but again, would m be the damping coefficient, and what would it's units be?

Thanks

2. Nov 8, 2011

### AlephZero

Start from the equation of motion including damping, and compare its solution with what you measured.

If the equation of motion for free damped vibration is $m\ddot x + c\dot x + kx = 0$, the general solution is of the form $e^{-pt} (A \cos \omega t + B \sin \omega t)$.

Any textbook or web site on SDOF should show you how p and $\omega$ are related to m, c, and k, if you don't want to work it out for yourself.