## Quick Reference

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 *θ* ≈ *θ* and the equation becomes *θ̈*+ω^{2}*θ*=0, where ω^{2}=*g*/*l*. It follows that the pendulum performs approximately simple harmonic motion with period

*Subjects:*
Mathematics.

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