# Pendulums

There are a number of different forms of pendulum. The main characteristic being that when the mass is displaced from it's position of rest it will oscillate at a fixed frequency.

- As used in the simplest mechanical clock designs.
- where
- τ = period [s]
*l*= length [m]*g*= gravitational acceleration [ms^{-2}]
Simple Pendulum |

- Note that it would be necessary to throw the bob into a circular motion to start it and then once settled the equation may be applied.
- where
- τ = period [s]
*l*= length [m]- α = cone half-angle [rad]
*g*= gravitational acceleration [ms^{-2}]
Conical Pendulum |

- Another simple design used in some types of clock.
- where
- τ = period [s]
*l*= length [m]*I*_{0}= moment of inertia of bob [kgm^{2}]*k*_{t}= torsional rigidity [Nm^{2}]
Torsional Pendulum |

### Historical Notes

**1581**Galileo uses his pulse to time the swinging of the lamps in the cathedral at Pisa. He concludes that the time for a lamp to swing does not depend on the angle through which it swings. This observation eventually leads to the development of pendulum clocks.

**See also: **Schuler Pendulum, Simple Harmonic Motion.

**Subjects: ** Physics