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)kx<sup>2</sup>, KE = (1/2)kA<sup>2</sup> - (1/2)kx<sup>2.</sup> PE = KE when (1/2)kx<sup>2</sup> = (1/2)k(A<sup>2</sup> - x<sup>2</sup>). x<sup>2</sup> = A<sup>2</sup> - x<sup>2.</sup> 2x<sup>2</sup> = A<sup>2.</sup> 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.