Equations of motion for disk and spring system

[Nikstykal]

Homework Statement

Thin uniform disk with radius r, mass m, and moment of inertia 0.5mr² is suspended from a cable line where one end is attached to a set point via a spring, and the other end is also attached to a spring but is moving in an upwards direction. Solve for the equations of motion in terms of x(t) and θ(t).
http://imgur.com/xYwVP79

Homework Equations

ΣF=ma, ΣT=Iα, F_s=kδ

The Attempt at a Solution

Used Newtons 2nd law in terms of rotational and translational inertia. δ₁ is change in length of left spring, δ₂ is change of length of right spring.

Translational: kδ₁ + kδ₂ - mg = mx"
Rotational: -kδ₁r + kδ₂r = 0.5mr²θ"

I set δ₁ = rθ and then I set δ₂ = x_IN-x

Substituted in and just rearranged each equation to have variables one side and constant terms on the other. Is that the correct way to work this problem? Thanks

 

[Nikstykal]

just in case anyone comes across this... δ1 is actually x-rθ and δ2 is x+rθ... then ΣF=ma turns into -k(x-rθ) - mg + k(x_in-x-rθ) = mx". do the same for rotation and torques then solve