In simple harmonic motion, at what displacement from the equilibrium position is the kinetic energy equal to the potential energy?

Answer and explanation

Correct answer: C. x = +/- A / sqrt(2)

  1. Step 1: Total energy E = (1/2) k A^2. Step 2. Potential energy U = (1/2) k x^2. Step 3. When K = U, U = E / 2 => (1/2) k x^2 = (1/4) k A^2 => x^2 = A^2 / 2 => x = +/- A / sqrt(2). Answer: x = +/- A / sqrt(2). Why not the others: At x = A/2, U = (1/4) E and K = (3/4) E.

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