A simple harmonic oscillator has amplitude A angular frequency ω and mass m . Then average kinetic energy in one time period is

Question

A simple harmonic oscillator has amplitude A angular frequency ω and mass m . Then average kinetic energy in one time period is, 1 2 m ω 2 A 2, 1 4 m ω 2 A 2, m ω 2 A 2, zero

MARKS App · Accepted Answer

Let displacement be x = A sin ω t + ϕ Kinetic energy, K = 1 2 m ω 2 A 2 cos 2 ω t + ϕ As the average value of cos 2 ω t + ϕ over a cycle is 1 2 . Therefore average kinetic energy is K a v = 1 4 m ω 2 A 2

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