# Homework Help: Equations of motion for disk and spring system

1. Feb 22, 2017

### Nikstykal

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

2. Relevant equations
ΣF=ma, ΣT=Iα, Fs=kδ

3. 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 = xIN-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

Last edited by a moderator: May 4, 2017
2. Feb 23, 2017

### 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