- θ max

- θ max + θ max Figure . A body (disc) allowed to rotate freely about an axis - - - - Unit Oscillations But α θ = d dt and therefore, d dt I θ κ θ   =− ( . ) This differential equation resembles simple harmonic differential equation. So, comparing equation ( .

) with simple harmonic motion given in equation ( . ), we have ω κ I rads  ( . ) The frequency of the angular harmonic motion (from equation . ) is I Hz = π κ ( .

) The time period (from equation . ) is I = π κ second ( . ) . .

Comparison of Simple Harmonic Motion and Angular Simple Harmonic Motion In linear simple harmonic motion, the displacement of the particle is measured in terms of linear displacement r  The restoring force is F kr =− , where k is a spring constant or force constant which is force per unit displacement. In this case, the inertia factor is mass of the body executing simple harmonic motion. In angular simple harmonic motion, the displacement of the particle is measured in terms of angular displacement  θ . Here, the spring factor stands for torque constant i.e., the moment of the couple to produce unit angular displacement or the restoring torque per unit angular displacement.

In this case, the inertia factor stands for moment of inertia of the body executing angular simple harmonic oscillation. Table . Comparision of simple harmonic motion and angular harmonic motion S.No Simple Harmonic Motion Angular Harmonic Motion . The displacement of the particle is measured in terms of linear displacement  The displacement of the particle is measured in terms of angular displacement  θ (also known as angle of twist).

. Acceleration of the particle is a   =− ω Angular acceleration of the particle is α ω θ =− . . Force, F m a , where m is called mass of the particle.

Torque, τ α = I , where I is called moment of inertia of a