- #1
Nikstykal
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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, Fs=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 = 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
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