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Mechanical Properties Of Fluids

Question
CBSEENPH11019230

A particle is executing simple harmonic motion. What is the ratio potential energy to kinetic energy when the displacement is 0.6A, where A is the amplitude of oscillation?

Solution

Kinetic energy of particle at a distance y from the meain position is,
K equals 1 half m omega squared left parenthesis A squared y squared right parenthesis
Potential energy of particle at a distance y from the mean  position is,
straight U equals 1 half mω squared straight y squared space
The ratio of potential energy to kinetic energy at a distance y from the mean position is,
space space space space space space space straight U over straight K equals fraction numerator left parenthesis 0.6 straight A right parenthesis squared over denominator straight A squared minus left parenthesis 0.6 straight A right parenthesis squared end fraction equals fraction numerator 0.36 over denominator 0.64 end fraction equals 9 over 16