Torsional Pendulum (Period)


Torsion balances, torsion pendulums and balance wheels are examples of torsional harmonic oscillators that can oscillate with a rotational motion about the axis of the torsion spring, clockwise and counterclockwise, in harmonic motion. (e.g. A Pendulum, the weight of which is rotated alternately in opposite directions through a horizontal plane by the torsion of the suspending rod or spring, used for clocks intended to run a long time between windings).
A balance spring, or hairspring, is a spring attached to the balance wheel in mechanical timepieces. It causes the balance wheel to oscillate with a resonant frequency when the timepiece is running, which controls the speed at which the wheels of the timepiece turn, and thus the rate of movement of the hands.
The balance spring provides a restoring couple that limits and reverses the motion of the balance so it oscillates back and forth. The motion of the balance is approximately simple harmonic motion.
A balance wheel’s period of oscillation , the time required for one complete cycle (two beats), is determined by the wheel’s moment of inertia and the stiffness (spring constant) of its balance spring.

Related formulas


TPeriod (s)
IMoment of inertia (kg*m2)
kTorsional rigidity (N*m)