Answer: A/sqrt(2).
- A A/sqrt(2)
- B A/2
- C A*sqrt(2)
- D A
Correct answer: A. A/sqrt(2)
Explanation: At displacement x: PE = (1/2)kx2, KE = (1/2)kA2 - (1/2)kx2. PE = KE when (1/2)kx2 = (1/2)k(A2 - x2). x2 = A2 - x2. 2x2 = A2. x = A/sqrt(2).
As a pendulum swings, total mechanical energy (KE+PE) stays constant: at the highest points A and C, all energy is potential (zero speed); at the lowest point B, all of that energy has converted into kinetic energy (maximum speed).
Concept context
Work-energy theorem, potential energy, conservation of energy, collisions.