In a mathematical model, a simple pendulum is represented by a particle of mass m, suspended by a light string of constant length l 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, acted on by gravity and tension in the string. Suppose the string makes an angle θ‎ with the vertical at time t. The equation of motion is $\ddot{\theta }+(g/l)\text{sin}\theta =0$. When θ‎ is small for all time, sin θ‎ ≈ θ‎ and the equation becomes $\ddot{\theta }+{\omega }^2\theta =0$, where ω‎² = g/l. It follows that the pendulum performs approximately simple harmonic motion with period $2\pi \sqrt{l/g}.$