Question

Derive an expression for velocity of a particle executing shm​

Answer 1

Answer:

here

Explanation:

you can observe the solution in supplement attached

Answer 2

An expression for velocity of a particle executing shm​ is :

• Simple Harmonic Motion is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position.

• Expression for position of a particle as a function of time is given as

x = A sin (ωt + Φ)

• Velocity is given as dx/dt

v = Aω cos (ωt + Φ)

= Aω √[ 1 - sin^2 (ωt + Φ) ]

x = A sin ωt

x^2 / A^2 = sin ^2 ωt

• v = Aω √ 1 - x^2 / A^2

= ω √ A^2 - x^2