Coupled Harmonic oscillator problem

[Reshma]

I need your help to solve this problem on coupled harmonic oscillators.

Two masses m1 and m2 are attached to two rigid supports by means of springs of force constants k1 and k2 respectively. The masses are connected to a third spring of force constant k3. The masses are free to move along the x-axis, assuming there is no damping. Set up the equations of motion for the system.

My work:

I suppose the third spring is connected in between the two masses.
Equation for first mass is:
$$m_1\ddot{x} = -k_1x$$
Equation for second mass is:
$$m_2\ddot{x} = -k_2x$$

Now please help me proceed to setup the equation for the 2 connected masses.

 

[stunner5000pt]

what you did didnt seem to cosnider the third spring
let it be in this order
k1 m1 k3 m2 k2 (thats how the steup would be, I am too lazy to draw a diagram)
suppose m1 was moved right or left) by some amount x1 then m2 may also move some amount x2 right?
i don't think it is necessary for x1 = x2.
so your equation is now (if i took the left direction to be positive)
$$m \ddot{x} = k_{1}x_{1} + k_{3}(x_{2}-x_{1})$$
$$m \ddot{x} = k_{2}x_{2} + k_{3}(x_{2}-x_{1})$$

thats my two cents
i think they may be a problem with the signs...