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  4. A very large (uniform disk) is connected to a very stiff spring as shown in figure. Spring is attached a distance d below the axle of the disc. System is in equilibrium in configuration shown. If disc is rotated through a small angle θ0=3° find the maximum kinetic energy of disc in joule. (. Given .K=900 N / m ; R=3 m ; d=2 m , π2=10)

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Q. A very large (uniform disk) is connected to a very stiff spring as shown in figure. Spring is attached a distance $d$ below the axle of the disc. System is in equilibrium in configuration shown. If disc is rotated through a small angle $\theta_{0}=3^{\circ}$ find the maximum kinetic energy of disc in joule.
$\left(\right.$ Given $\left.K=900\, N / m ; R=3\, m ; d=2\, m , \pi^{2}=10\right)$Physics Question Image

Oscillations

Solution:

$(k d \theta) d=\left(\frac{M R^{2}}{2}\right) \alpha$
$\alpha=-\left(\frac{2 k d^{2}}{M R^{2}}\right) \theta ; K \cdot E_{\cdot \max }=\frac{k d^{2} \theta_{0}^{2}}{2}$