A torsional pendulum consists of an object suspended by a wire of a certain stiffness. The object is turned through an angle and released from rest, resulting in the harmonic motion of the object rotating back and forth. This Demonstration illustrates this type of harmonic motion, which follows Newton's second law for rotations,
. The torque of this pendulum is directly proportional to the angle it is turned by a factor of the torsional constant, which is a measure of the stiffness of the wire. Since
,
, which is a second-order differential equation. The solution of this equation as a function of time is
, where
is the angular frequency.
