Homework Help: Simple Harmonic Motion: Two Springs One Mass

1. Oct 7, 2012

TheRedDragon

1. The problem statement, all variables and given/known data

Two springs each have spring constant k and equilibrium length (L). They are both stretched a distance (L) and attached to a mass m and two walls.

At a given instant, the right spring constant is somehow magically changed to 3k (the relaxed length remains L). what is the resulting x(t)?

Take the initial Position to be x=0

2. Relevant equations

3. The attempt at a solution

My problem is figuring out the Force equations of the system.

Could it be:
F(spring system) = -kx-3kx
where the 2L lengths on each side of the mass doesn't matter

or
F(spring system) = -k(2L+x)-3k(2L-x)
where the 2L lengths on each side of the mass does matter

or

Something else that I'm not considering.

I'm confused because the textbook doesn't have example problems on a similar system of two springs one mass. Also, my second guess would make a really complicated differential equation, where I don't think I could use use a guess such x(t)=Ae^(alpha*t) because there is a constant in the equation.

Can someone explain to me the correct equation for the spring force?