simple pendulum

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In a mathematical model, a simple pendulum is represented by a particle of mass m, suspended by a string of constant length l and negligible mass from a fixed point. The particle, representing the bob of the pendulum, is free to move in a specified vertical plane through the point of suspension. The forces on the particle are the uniform gravitational force and the tension in the string. Suppose the string makes an angle θ with the vertical at time t. The equation of motion can be shown to give θ̈+(g/l) sin θ=0. When θ is small for all time, sin θθ and the equation becomes θ̈2θ=0, where ω2=g/l. It follows that the pendulum performs approximately simple harmonic motion with period

Subjects: Mathematics.

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