# An Angular Simple Harmonic Oscillator

An Angular Simple Harmonic Oscillator

shows an angular version of a simple harmonic oscillator; the element of  springiness or elasticity is associated with the twisting of a suspension wire  than the extension and compression of a spring as we previously had. The devic called a torsion pendulum, with torsion referring to the twisting.

If we rotate the disk in by some angular displacement e from its position (where the reference line is at e = 0) and release it, it will oscillate at that position in angular simple harmonic motion. Rotating the disk through angle e in either direction Introduces a restoring torque given by Here K (Greek kappa) is a constant, called the torsion constant, that depends the length, diameter, and material of the suspension wire Comparison of  with leads us to suspect that  the angular form of Hooke’s law, and that we can transform which the period of linear SHM, into an equation for the period of angular SHM replace the spring constant k in with its equivalent, the constant and we replace the mass m in  with its equivalent, the inertial of the oscillating disk. These replacements lead to which is the correct equation for the period of an angular simple harmonic oscillator or torsion pendulum. An angular simple harmonic oscillator, or torsion pendulum, is an angular version of the linear simple harmonic oscillator of The disk oscillates in a horizontal plane; the reference line oscillates with angular amplitude 8m, The twist in the suspension wire stores potential energy as a spring does and provides the reo storing torque