A gravity pendulum is a weight on the end of a rigid or flexible line or rod, which, when given some initial lift from the vertical position, will swing back and forth under the influence of gravity over its central (lowest) point. A torsion pendulum consists of a body suspended by a fine wire or elastic fiber in such a way that it executes rotational oscillations as the suspending wire or fiber twists and untwists.
For small displacements, the movement of an ideal pendulum can be described mathematically as simple harmonic motion, as the change in potential energy at the bottom of a circular arc is nearly proportional to the square of the displacement. Real pendulums do not have infinitesimal displacements, so their behavior is actually non-linear. Real pendulums will also lose energy as they swing, and so their motion will be damped, with the size of the oscillation decreasing approximately exponentially with time.
In the case of a pendulum with a point mass swinging on massless string or rod of length l, and an ambient gravity acceleration of g, the period of a complete oscillation is
Notice that the equation for T is independent of the bob's mass. This can be considered a consequence of the equivalence of gravitational mass and inertial mass: a heavier bob has a stronger restoring force, but on the other hand has more inertia and the two effects cancel.
The presence of g in the equation means that the pendulum frequency is different at different places on earth. So for example if you have an accurate pendulum clock in Glasgow (g=981.563 cm/s/s) and you take it to Cairo (g=979.317 cm/s/s), you must shorten the pendulum by 0.23%.
Two coupled pendulums form a double pendulum.
If I is the moment of inertia of a body with respect to its axis of oscillation, and if K is the torsion coefficient of the fivre (torque required to twist it through an angle of one radian), then the period of oscillation of a torsion pendulum is given by
See also: Foucault's pendulum, pendulum clock, pendular, physics.
Pendulum is a trade name for a preemergent herbicide used for control of crabgrass in turf. Its active ingredient is pendimethalin.