Question

What is the displacement of an object in SHM when the K.E and P.E are equal

Answer 1

Answer:

The displacement of the object in SHM is ±A/√2

Explanation:

The K.E of a particle executing SHM is given by,

KE = ½ mω² (A² – y²)

where

m denotes the mass of the particle

ω denotes the angular velocity of the particle

A denotes the amplitude

y denotes the displacement

The P.E of a particle executing SHM is given by,

PE = ½ mω²y²

where

m denotes the mass of the particle

ω denotes the angular velocity of the particle

y denotes the displacement

Given, KE and PE are equal.

KE = PE

½ mω² (A² – y²) = ½ mω²y²

A² – y² = y²

A² = y² + y²

A² = 2y²

y² = A²/2

y = √(A²/2)

$\tt \longrightarrow y = \pm \dfrac{A}{\sqrt{2}}$