Question

What is steady state solution of a forced oscillsation system?

Answer 1

The equation of motion for a driven damped oscillator is:

md2xdt2+bdxdt+kx=F0cosωt.

We shall be using ω for the driving frequency, and ω0 for the natural frequency of the oscillator (meaning that ignoring damping,  so ω0=√k/m. )

external driving force = F0eiωt

with F0 real, so the actual physical driving force is just the real part of this, that is, F0cosωt.

So now we’re trying to solve the equation

md2xdt2+bdxdt+kx=F0eiωt.

Answer 2

Explanation:

The solution to the driven harmonic oscillator has a transient and a steady-state part. The steady-state solution is the particular solution to the inhomogeneous differential equation of motion. It is determined by the driving force and is independent of the initial conditions of motion.