Physics
Physics
Problem
Suppose the amplitude of a block–spring oscillator is doubled while the mass and spring constant remain unchanged. Which of the following describes how the block’s maximum kinetic energy changes? a) It increases by a factor of 2. b) It does not change. c) It increases by a factor of 4. d) It decreases by a factor of 2.Intuitive explanation
The key insight is that maximum kinetic energy depends on how much elastic potential energy the spring stores at maximum displacement. When you double the amplitude, the spring stretches twice as far, so it stores four times as much potential energy (since ). By energy conservation, all that potential energy converts to kinetic energy at equilibrium, so the maximum kinetic energy increases by a factor of four.
Intuitive explanation
The key insight is that maximum kinetic energy depends on how much elastic potential energy the spring stores at maximum displacement. When you double the amplitude, the spring stretches twice as far, so it stores four times as much potential energy (since ). By energy conservation, all that potential energy converts to kinetic energy at equilibrium, so the maximum kinetic energy increases by a factor of four.