Equation of SHM: Practice Problem & Solution
A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is \(3\) times the weight of the pendulum bob. What is the maximum angular displacement of the pendulum of the string with respect to the vertical ?
Solution Explained:
To solve this problem, we apply the core principles of Equation of SHM. Understanding the underlying formula is key to arriving at the correct answer below:
At the mean position, tension is \(T = mg + \frac{mv^2}{L}\). Given \(T = 3mg ⇒ \frac{mv^2}{L} = 2mg ⇒ v^2 = 2gL\). Using conservation of energy, \(mgL(1 - \cos\theta) = \frac{1}{2}mv^2 = mgL ⇒\cos\theta = 0 ⇒ \theta = 90^\circ\).
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