Question

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

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Solution

Total energy of particle executing simple harmonic motion is,

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Therefore kinetic energy at position is,

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Therefore kinetic energy at position half the amplitude of oscillation is,

straight K space equals space 1 half m omega squared open square brackets straight A squared minus open parentheses straight A over 2 close parentheses squared close square brackets space space space space space equals 1 half m omega squared open parentheses 3 over 4 straight A squared close parentheses space space space space equals 3 over 4 straight E

Now fraction of the total energy, which is kinetic is,

straight K over straight E equals 3 over 4

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Mechanical Properties Of Fluids

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