A mass-spring system executes simple harmonic motion with amplitude A. At what displacement x from equilibrium is the kinetic energy equal to the potential energy?
Answer and explanation
Correct answer: C. x = A / sqrt(2)
- Step 1: Total energy is 0.5kA^2. Kinetic energy is 0.5k(A^2 - x^2) and potential energy is 0.5kx^2. Step 2. Equating them gives A^2 - x^2 = x^2, so 2x^2 = A^2, yielding x = A / sqrt(2). Answer: x = A / sqrt(2). Why not the others:* At x = A/2, potential energy is only one quarter of the total energy.
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