Find the steady-state motion of the mass–spring system modeled by the ODE:
for a diff eq modeled as: my''+cy'+ky=F0cos(ωt),
The Attempt at a Solution
I'm really not sure how to solve this since the equation given is not in the correct form (the right side is not in the form F0cos(ωt)).
Just to attempt the problem, I ignored the 225 and pretended that the right side was -75cos(3t)
m=4, c=12, k=9, F0=-75, ω=3, ω0=3/2
plugging in these values for a and b:
which would make the (incorrect) solution: yp=cos(3t)-(4/3)sin(3t)
The book's answer is: yp=25+(4/3)cos(3t)+sin(3t)
Is there another formula I should be using? The book has several other formulae listed for the chapter but doesn't explain them very well...