Question

What is meant by damping or dissipative force? Establish the differential equation of a damped harmonic oscillator and solve it to obtain an expression for the displacement of the oscillator.

Answer 1

Dissipative force The dissipative force is a force in which work done by the force is negative, and in this energy always be losses.

$$F _ d ​ =−bv$$

$$F =ma =−kx−mbv$$

$$\omega^2=\frac{k}{m}-\frac{b^2}{4m^2}$$

$$x=Ae^{-\frac{bt}{2m}}\cos{(\omega t+\phi_0)}$$