$\tau_{net} = J_0 \alpha = Tr + F_s R$
Hooke's law for an ideal linear spring says ...
$F_s = -kx$
recall arc length equals radius times angular displacement ...
$x = R \cdot \Delta \theta$
$R = 4r$ and $\Delta \theta = \theta_0 + \theta$, where $\theta_0$ is the angular displacement of the pulley at system equilibrium, and $\theta$ is the additional angular displacement beyond equilibrium to induce an oscillation of the system.
$F_s R = -k \color{blue}{x} \cdot \color{red}{R} = -k \cdot \color{blue}{4r(\theta_0+\theta)} \cdot \color{red}{4r}$
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Last edited by skeeter; Jul 13th 2017 at 06:36 AM.
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