A body oscillates with simple harmonic motion of amplitude A . What fraction of its total mechanical energy is kinetic energy when its displacement from the mean position is (A)/(3) ?

Question

Quantrex Academy · Accepted Answer

Correct answer: D. (8)/(9)

Total mechanical energy of a simple harmonic oscillator is

E = \dfrac{1}{2} m \omega^2 A^2

Kinetic energy at a displacement

x

is

K = \dfrac{1}{2} m \omega^2 (A^2 - x^2)

The fraction of kinetic energy to total energy is

\dfrac{K}{E} = \dfrac{A^2 - x^2}{A^2} = 1 - \left(\dfrac{x}{A}\right)^2

Substituting

x = \dfrac{A}{3}

:

\dfrac{K}{E} = 1 - \left(\dfrac{1}{3}\right)^2 = 1 - \dfrac{1}{9} = \dfrac{8}{9}

Answer:

\dfrac{8}{9}

A body oscillates with simple harmonic motion of amplitude A . What...

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