A particle is executing linear simple harmonic motion of amplitude A. What

Question

A particle is executing linear simple harmonic motion of amplitude A. What fraction of the total energy is kinetic when the displacement is half the amplitude?

Options:

A . 14

B . 12√2

C . 12

D . 34

Answer: Option D
:
D
Kinetic energy

(K E) = \frac{1}{2} m ω^{2} (A^{2} - x^{2})

Potential energy

(P E) = \frac{1}{2} m ω^{2} x^{2}

Total energy

(E) = \frac{1}{2} m ω^{2} A^{2} W h e n x = \frac{A}{2}

KE =

\frac{1}{2} m ω^{2} (A^{2} - \frac{A^{2}}{4}) = \frac{3}{8} m ω^{2} A^{2} E = \frac{1}{2} m ω^{2} A^{2} ∴ \frac{K E}{E} = \frac{3}{4}

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