pendulum Any rigid body that can execute simple harmonic oscillations about an axis. A simple pendulum is a bob suspended from a rigid support with an elastic string of negligible mass. The time period of oscillation, T with small amplitude, is given by,
T=2p [l /g]1/2
where l is the length of the string.
A compound pendulum is a rigid body that executes simple harmonic oscillations under the action of gravity, about a horizontal axis passing through it. The time period, T of oscillation, for small amplitude is given by,
T=2p [(k2 + h2) /(hg) ]1/2
where k is the radius of gyration* , and h is the distance between center of mass and the axis.
In a torsional pendulum a disc of moment of inertia I is suspended by a suspension fiber at its axis. The disc executes simple harmonic oscillations under the action of shear restoring force. The time period of oscillation, T is given by,
T=2p [ 2 I l (f a4 p ) ]1/2
where l is the length of the fiber, a the radius of the fiber and f the shear modulus.