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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.

Table of Contents:

## Formula

**t = 2pi sqrt (l I _{0} / k_{t})**

**Where,**

pi = Constant (3.14)

t = Period [s]br

l = Length of the spring [m]

I

_{0}= Moment of Inertia of Bob [kgm

^{2}]

k

_{t}= Torsional Rigidity [Nm

^{2}]

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 I_{0} = 15kgm^{2}

Torsional Rigidity k_{t} = 10 Nm^{2}

**Solution:**

**Apply Formula:**

t = 2pi sqrt (l I_{0} / k_{t})

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**