At what distance is the kinetic energy of particle performing SHM of amplitude 10cm three times its PE?

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At what distance from the mean position is the kinetic energy of a particle performing S.H.M. of amplitude 8 cm, three times its potential energy?

Data: A = 8 cm, KE = 3 PE

KE = `1/2`k(A2 − x2) and PE = `1/2`kx2

Given, KE = 3PE.

∴ `1/2`k(A2 − x2) = `3(1/2"kx"^2)`

∴ A2 − x2 = 3x2

∴ 4x2 = A2

∴ the required displacement is

x = `±"A"/2=±8/2` = `±` 4 cm

Concept: Amplitude (A), Period (T) and Frequency (N) of S.H.M.

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