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?
(a) Let w(t)=y(t)-y0/k. Then y(t)=w(t)+y0/k. Since y0 and k are constants, then we ...
This shows how to rewrite a forced harmonic oscillator. Forced harmonic equations are examined.