# Nonlinearized Motion of a Simple Pendulum

Nonlinearized Motion of a Simple Pendulum

The motion of a simple pendulum is governed by the nonlinear equation , where is the acceleration due to gravity and is the length of the pendulum. This is the equation that this Demonstration models. In contrast, for small , , which gives the linear equation .

θ''+g/Lsin(θ)=0

g

L

θ

sin(θ)≈θ

θ''+g/Lθ=0

This approximate solution can be made visible, so it may be compared to the exact solution and the conditions under which the approximation is valid can be studied.