A glider on a virtually friction-free air track is connected to a spring and…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A glider on a virtually friction-free air track is connected to a spring and undergoes simple harmonic motion along a straight line. The velocity–time graph of the glider is described as follows.
• The graph is sinusoidal with period T=1.20s.
• The positive velocity maximum is +0.60ms−1 and occurs at t=0.30s.
• The velocity is zero at t=0.
Assume the equilibrium position corresponds to x=0.
(a) Determine the amplitude A of the glider’s displacement. Show your reasoning.
(b) Write an explicit expression for the displacement x(t) that is consistent with the velocity graph. Your expression must include a phase constant chosen so that the predicted velocity matches the given description.
(c) Calculate the magnitude of the glider’s maximum acceleration amax.
(d) Using your expression from part (b), compute both the displacement and the velocity of the glider at t=1.50s. Include proper units with your answers.