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According to MyPhysicsLab, the equation of motion for the pendulum is :
θ'' = -(g/R) sin θ
For small oscillations we can use the approximation that sin θ = θ.
Then the equation of motion becomes :
θ'' = -(g/R) θ
This is a linear relationship. The analytic solution is :
θ(t) = θ0 cos(sqrt(g/R) t)
where θ0 is the initial angle.
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