Pendulum Cord Tension


A pendulum consists of a weight of mass m, called a bob, on a cord of length L and negligible mass. Initially the pendulum is held such that the cord is tight and horizontal. What is the tension in the cord as a function of the angle (q) through which the pendulum has descended after it is released.


The velocity of the bob at any point in the swing will be such that the change in kinetic energy 1/2*m*v2 is equal to the change in potential energy of m*g*L*sin(q), or
v2=m*g*L*sin(q)/(1/2*m), or
The centripetal acceleration at any point in the swing will be v2/L=2*g*sin(q).

The acceleration due to gravity is g, so the component contributing to tension in the cord is g*sin(q). The tension in the cord is the mass of the bob times the acceleration provided by the cord, or

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