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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.

m
kgm2
Nm2
t

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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