- #1

- 75

- 0

## Homework Statement

Find the steady-state motion of the mass–spring system modeled by the ODE:

4y''+12y'+9y=225-75sin(3t)

## Homework Equations

for a diff eq modeled as: my''+cy'+ky=F

_{0}cos(ωt),

y

_{p}=acos(ωt)+bsin(ωt)

a=F

_{0}*(m(ω

_{0}

^{2}-ω

^{2}))/(m

^{2}*(ω

_{0}

^{2}-ω

^{2})

^{2}+ω

^{2}c

^{2})

b=F

_{0}*(ωc)/(m

^{2}*(ω

_{0}

^{2}-ω

^{2})

^{2}+ω

^{2}c

^{2})

## 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 F

_{0}cos(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, F

_{0}=-75, ω=3, ω

_{0}=3/2

plugging in these values for a and b:

a=1, b=-4/3

which would make the (incorrect) solution: y

_{p}=cos(3t)-(4/3)sin(3t)

The book's answer is: y

_{p}=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...