Question

A particle is oscillating in SHM. What fraction of total energy is kinetic when the particle is at A/2 from the mean position (A is the amplitude of oscillation).​

Answer 1

Refer to the attachment please

Answer 2

Concept:

• Simple Harmonic Motion
• Conservation of mechanical energy

Given:

• The particle is at a distance of A/2 from the mean position
• A is the amplitude of the oscillation

Find:

• The fraction of total energy which is kinetic

Solution:

v is the velocity of the particle and w is the angular velocity of the particle

$v =w \sqrt{A^{2} - y^{2} }$

Total energy E

$E = 1/2 mw^{2} A^{2}$

Kinetic energy at A/2

$KE = 1/2mv^{2} \\KE = 1/2mw^{2} (A^{2} -y^{2} )$

KE/E = (A²-y²)/A²

y = A/2

KE/E = 3/4

3/4 of the total energy is kinetic.

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