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Thin rod of length $L$ and mass $M$ is frec to rotate in a vertical plane about a horizontal axis passing through the point $O$ where one end of the rod is pivoted as shown in figure. The other end of the rod is connected to a vartical massless spring of force constant $k .$ The lower end of the vertical spring is rigidly fixed to the ground at $G$. When the rod is in equilibrium position it is parallel to the ground. When the rod is slighuly rotated from its cquilibrium position and relcased,
(a) Find its time period $T$ of small oscillations.
(b) What will be the maximum linear speed of the displaced end of the rod if the amplitude of oscillations is taken $\theta_{0}$ ?