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Forced harmonic oscillator

Consider the forced harmonic oscillator:
y'' + by' + ky = g(t) + y0
where the forcing is made up of two parts, constant forcing (y0) and forcing (g(t)) that changes over time.
a) Let w(t) = y(t) - y0/k. Rewrite the forced harmonic oscillator equation in terms of the new variable w.
b) In what ways are the solutions of the two equations the same?

Solution Preview

(a) Let w(t)=y(t)-y0/k. Then y(t)=w(t)+y0/k. Since y0 and k are constants, then we ...

Solution Summary

This shows how to rewrite a forced harmonic oscillator