Question

A simple harmonic oscillator has amplitude 'A'.
If the kinetic energy of oscillator is
one-fourth of the total energy, then the
displacement is
(A) AV
(B) V3 A/2
(C) A/4
(D) A/2​

Answer 1

Answer:

AV this is my answer hgsftwyoihfryi

Answer 2

Answer :

Amplitude of motion = A

We have to find displacement of simple harmonic oscillator from mean position at where kinetic energy of oscillator becomes one-fourth of the total energy$.$

★ P.E. at displacement x from the mean position,

• U = 1/2 kx²

★ K.E. at displacement x from the mean position,

• K = 1/2 k (A² - x²)

★ Total energy at any point

• E = K + U = 1/2 kA²

where A denotes amplitude

Let p be the point at where kinetic energy becomes one-fourth of the total energy.

➠ E/4 = K

➠ 1/2 kA² = 4 × [1/2 k (A² - x²)]

➠ A² = 4A² - 4x²

➠ 4x² = 3A²

➠ x² = 3A²/4

➠ x = √3A/2

∴ (B) is the correct answer.