Torsional Pendulum Calculator

Torsional Pendulum refers to a torsion spring that works by torsion or twisting that is, a flexible elastic object that stores mechanical energy when it is twisted. A torsion pendulum is a mass suspended on a string (or torsion fiber) that rotates periodically. When the mass of a torsion pendulum is rotated from its equilibrium position, the fiber resists the rotation and provides a restoring force that causes the mass to rotate back to its original equilibrium position. When the mass reaches its equilibrium position, it is moving quickly and overshoots.

Torsional Pendulum

Length of the spring m
Moment of inertia of bob kgm2
Torsional rigidity Nm2
Period t
Formula
t = 2pi sqrt (l I0 / kt)

Where,
pi = Constant (3.14)
t = Period [s]br
l = Length of the spring [m]
I0 = Moment of Inertia of Bob [kgm2]
kt = Torsional Rigidity [Nm2]
Torsion Pendulum is a device consisting of a disk or other body of large moment of inertia mounted on one end of a torsionally flexible elastic rod whose other end is held fixed; if the disk is twisted and released, it will undergo simple harmonic motion, provided the torque in the rod is proportional to the angle of twist.

Example:
Calculate the oscillation period of Torsion Pendulum for the given details.
Length of the Spring 1 = 25 m
Moment of inertia of bob I0 = 15kgm2
Torsional Rigidity kt = 10 Nm2

Solution:
Apply Formula:
t = 2pi sqrt (l I0 / kt)
t = 2*3.14 sqrt (25*15/10)
t = 6.18 sqrt (375/10)
t = 6.18 sqrt (37.5)
t = 6.18*6.12
t = 38.4569889616959 t
Period (t) = 38.4569889616959 t