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Question
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?
Solution
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
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