A2 Daily A Level Physics question
A glider attached to a horizontal spring oscillates on an air track with negligible friction. In a second run, the glider is pulled to twice the initial amplitude (from 3.0 cm to 6.0 cm) and released from rest, with the same mass and spring. What happens to the maximum kinetic energy in the subsequent motion?
Answer
The correct answer is C.
Correct: C — It increases by a factor of 4 compared with the first run. In SHM the total mechanical energy, and hence the maximum kinetic energy (at equilibrium), is proportional to the square of the amplitude, so doubling amplitude gives 2^2 = 4 times the energy. A is wrong because doubling amplitude does not just double the energy; it scales with amplitude squared. B is wrong because a factor of 8 implies a cubic dependence, which is not the case. C is correct as energy ∝ amplitude^2, so doubling gives four times. D is wrong because even though the period is unchanged, the energy depends on amplitude and thus increases when the amplitude is larger.