A block attached to an ideal horizontal spring executes one–dimensional oscillations…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A block attached to an ideal horizontal spring executes one–dimensional oscillations on a frictionless surface. A verbal description of the block’s position–versus–time graph is provided below.
• At t=0, the block is at its maximum positive displacement x=+0.080m.
• The block first passes through the equilibrium position moving toward negative x at t=0.25s.
• The motion is sinusoidal and repeats every 1.0s.
Use this information to analyze how the velocity–time and acceleration–time graphs are related to the given position–time graph.
(a) Identify all times during the first full cycle (0≤t≤1.0s) at which the block’s velocity reaches its positive maximum. Justify your answer using features of the position–time graph.
(b) Sketch a qualitative velocity–time graph for one full cycle on blank axes you provide. Clearly label the time axis with numerical values (every 0.25s) and indicate the magnitude of the velocity extrema. Explain how you determined the phase relationship between the displacement and velocity graphs.
(c) On a second set of axes, sketch the acceleration–time graph for the same interval. Describe in words why this graph is inverted relative to the displacement graph and why its extrema occur where they do.