# Homework Help: Coupled Oscillators

1. Nov 12, 2014

### NATURE.M

1. The problem statement, all variables and given/known data
1. Note this question is from Morin 4.35. The system in the example in Section 4.5 is modified by subjecting the
left mass to a driving force Fd*cos(2ωt), and the right mass to a driving
force 2Fd cos(2ωt), where ω^2 = k/m. Find the particular solution for x1 and x2.

Just to note the equations of motion of the example in section 4.5 are:
x ̈1 + 2*ω2*x1 − ω2*x2 = 0
x ̈2 + 2*ω2*x2 − ω2*x1 = 0
3. The attempt at a solution

So the equations of motion with driving are :
x ̈1 + 2*ω2*x1 − ω2*x2 = (Fd/m)*cos(2wt)
x ̈2 + 2*ω2*x2 − ω2*x1 = (2Fd/m)*cos(2wt)

I add and subtract the above differential equations and obtain:

z'' + w^2 * z = (3Fd/m) *cos(2wt), where z = x1 + x2
z'' + 3w^2 * z = (-Fd/m)*cos(2wt), where z = x1 - x2

Then using z = Acos(2wt) and z = Bcos(2wt) as solutions to the above equations we end up with:
A= -Fd/k and B=Fd/k.

From here solving for x1 and x2 yields: x1 = 0 and x2 = (-Fd/k)*cos(2wt).
This makes no sense to me, but it seems to be the only solution I'm getting.

2. Nov 12, 2014

### rude man

For openers, using z to represent two different parameters is not a good idea.
Also, you shoud have stated the original problem 4.35 in full.