# Velocity of a Pendulum

by Noir
Tags: pendulum, velocity
 P: 413 The equation is wrong, firstly because it is dimensionally incorrect. The dimensions of the RHS do not match the dimensions of the LHS. Secondly, if you take the pendulum to a height 'h' and then release it, it is a very simple observation that, the speed at any point will be higher if 'h' is made higher. But, the equation above does not include any term of the initial height. Also, at an height equal to the maximum height of the oscillating pendulum i.e. at it's amplitude, the velocity should be zero. The given formula does not account for it. A formula for the velocity can be easily derived, and I'd like you to try that. Use the law of conservation of energy and apply it to the case when the bob is at it's highest point and then to a arbitrary point [Basically, Gravitational Potential Energy is manifested as Kinetic Energy]. The formula I came at was: $$v = \sqrt{\frac{2gl}{m} (\cos(\theta) - \cos(\theta_o))}$$ here, 'l' is the length of the string and $\theta_o$ is the angle made when the pendulum is at it's highest.