Consider a simple pendulum oscillating in a vertical plane, with representing its angular displacement. If the mass of the bob is m , the tension in the string is equal to mg

Step-by-step solution

Let T be the tension in the string, m be the mass of the bob, v be its velocity, and L be the length of the pendulum. The forces acting on the bob in the radial direction are the tension T directed towards the pivot and the component of weight mg directed away from the pivot. Using Newton's second law for circular motion, the net radial force provides the necessary centripetal acceleration: T - mg = mv^2 L T = mg + mv^2 L For the tension to be equal to mg , the centripetal term must be zero: mv^2 L = 0 v = 0 The ve