Mass on a Wheel: Solve for Displacement After 100ms

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Homework Statement



All masses and radiuses given. (lets say 1m and 1kg for all)
A vertical wheel is free to spin without friction. Mass placed at the edge of the wheel (ie level with the centre) and is released, causing it to accelerate due to torque:

O'question asks what the vertical displacement of the point mass is after 100 milliseconds.

Homework Equations



I'm having trouble with nonlinear acceleration?
Anyone point me in the right direction?

The Attempt at a Solution



I tried assuming constant acceleration but that's not right.****EDIT: Misread question*****
I'll leave it up anyway
 
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So did you solve it or still need help?