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Consider a particle undergoing an SHM of amplitude A & angular frequency w. What is the magnitude of displacement from the mean position when kinetic energy is equal to the magnitude of potential energy?

Consider a particle undergoing an SHM of amplitude A & angular frequency w. What is the magnitude of displacement from the mean position when kinetic energy is equal to the magnitude of potential energy? Correct Answer A/√2

Let x = Asin(wt). ∴ Kinetic energy = 1/2 mA2w2cos2(wt) potential energy = 1/2kA2sin2(wt). According to given conditio1/2mA2w2cos2(wt) = 1/2A2w2sin2(wt) using, k = mw2, we get: tan2(wt) = 1. ∴ wt = π/4. ∴ x = Asin(π/4) = A/√2.

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