A horizontal mass–spring system oscillates with amplitude and maximum speed
PHYSICS · Single correct · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A horizontal mass–spring system oscillates with amplitude A and maximum speed vmax. The amplitude is then increased to 2A without changing the mass or spring constant. Which statement correctly compares the maximum kinetic energy in the new oscillation to that in the original oscillation?
(a) It is unchanged, because the maximum kinetic energy depends only on the mass and spring constant.
(b) It doubles, since the maximum speed doubles when the amplitude doubles.
(c) It quadruples, because total mechanical energy—and thus the maximum kinetic energy—is proportional to the square of the amplitude.
(d) It increases by a factor of eight, because both the amplitude and the maximum speed double.