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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

y"+by'+ky=g(t)+y0.
(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

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