In damped SHM, how do we know the motion has a single constant frequency throughout — without assuming it from the start? – physics.stackexchange.com
CR7 FAN
In damped SHM, we write:
$$m\ddot{x} + b\dot{x} + kx = 0$$
The standard approach assumes a solution of the form $e^{\alpha t}$
and derives:
$$\omega_d = \sqrt{\frac{k}{m} - \frac{b^2}{4m^2}}.$$
But ...