# Simulation of oscillator with frequency dependent damping

What would be the equation for the frequency dependent damping of harmonic oscillator? Is there something like:

$$\ddot{x}+2\delta\dot{x}+\omega_0^2x = \frac{F}{m}f(t)$$

with frequency dependent damping? Of course, it could be done by stating $\delta=\delta(\omega)$, but

• is there an example from mathematical physics where something like this arises from equation of motion?
• what is the physics behind?

Note 1: This question is motivated by sound synthesis task, but I am looking for physical backround. Therefore it's not engineering nor computational science.