Theory of Damping: General Equation?

[Gackhammer]

Is there a general equation of damping? I know that there is a second ODE for damping with regards to springs, and with RLC circuits, but is there a general form of damping equations (with critical-damp, overdamp, and under-damp). I know how to solve second ODEs, but I was wondering if there was a general equation, because all I could find are equations that relate specifically to springs or RLC Circuits

 

[AlephZero]

Try google for multi degree of freedom (MDOF) systems analysed using normal modes.

A general equation in that form is $\ddot x + 2\beta\omega\dot x + \omega^2 x = f$ where $\beta$ is < 1, = 1 or > 1 for under damping, critical, or over damping and $\omega$ is the undamped oscillation frequency.

 

[rbj]

it's the same as with RLC or the mechanical spring, mass, and dashpot models.

just a simple 2nd order differential eq.