Question

Describe the equation mx + cx + kx = 0?. And does this equation has any implications on the wave motion?.

Answer 1

The equation of motion describing the damped free vibrationsof a system with viscous damping is :

$m\overset{••}{x}+ c\overset{•}{x}+kx=0$

where $c$ is a constant called the coeficient of viscous damping.

Let us define a critical damping coefficient $c$

$2m\sqrt{\frac{k}{m}}=2m\omega_n$

where $\omega_n$ is the natural frequency of the system in the absence of damping

So, this equation describes the wave equation having damped oscillations.