The simple pendulum

A point mass hanging from an inextensible string oscillates in a vertical plane under gravity. Resolving the weight along the tangent to the trajectory gives the equation of motion; for small amplitudes it linearises into that of a harmonic oscillator, with a period that depends only on the length of the string and on $g$. For large amplitudes the isochronism breaks down.

• Forces and the equation of the pendulum
• Small oscillations and period
• Large amplitudes: correction to the period

Try it — interactive simulation

Change length, mass and gravity and verify that for small oscillations the period depends only on length, not on amplitude or mass.