Question

Write down the difference between simple harmonic motion and angular simple harmonic motion.

Answer 1

Comparison of simple harmonic motion and angular harmonic motion

S. No.	Simple Harmonic Motion	Angular Harmonic Motion
1.	The displacement of the particle is measured in terms of linear displacement `vec"r"`.	The displacement of the particle is measured in terms of angular displacement `vecθ` (also known as angle of twist).
2.	Acceleration of the particle is `vec"a" = -ω^2vec("r")`	Angular acceleration of the particle is `vecα = -ω^2vecθ`
3.	Force, `vec"F" = "m"vec"a"`, where m is called mass of the particle.	Torque, `τ = "I"vecα`, where I is called the moment of inertia of a body.
4.	The restoring force `vec"F" = -"k"vec"r"`, where k is restoring force constant.	The restoring torque `τ = -κvecθ`, where the symbol κ (Greek alphabet is pronounced as 'kappa') is called restoring torsion constant. It depends on the property of a particular torsion fiber.
5.	Angular frequency, `ω = sqrt("k"/"m")` rad s−1	Angular frequency, `ω = sqrt(κ/"I")` rad s−1