The harmonic oscillator's equation of motion is:
x'' + 2βx' + ω02x = f
with the forcing of the form f(t) = f0sin(ωt)
The Attempt at a Solution
So I got:
X1 = x
X1' = x' = X2
X2 = x'
X2' = x''
∴ X2' = -2βX2 - ω02X1 + sin(ωt)
The function f(t) is making me doubt this answer because I have to take into account f0 and it just disappears in the solution.
(For context I have to put it into a system of first order ODEs because I have to code it into python and plot the results with the given parameters.)
Am I on the right track? Or am I missing anything?