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.

Simple Pendulum
As used in the simplest mechanical clock designs.
where
τ = period [s]
l = length [m]
g = gravitational acceleration [ms-2]
Conical 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]
Torsional Pendulum
Another simple design used in some types of clock.
where
τ = period [s]
l = length [m]
I0 = moment of inertia of bob [kgm2]
kt = torsional rigidity [Nm2]
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.

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Subjects: Physics