A physics student compares the motion of an identical mass–spring system in two…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A physics student compares the motion of an identical mass–spring system in two different environments.
• Environment 1: The mass hangs from the spring in a laboratory on Earth.
• Environment 2: The same mass–spring system is taken aboard a spacecraft that is coasting in deep space far from massive bodies, so the local gravitational field is effectively zero.
In both environments the mass is displaced slightly downward from its respective equilibrium position and released from rest so that it executes small oscillations along the spring’s axis.
(a) For the arrangement on Earth, describe the forces acting on the mass when it is held at its equilibrium position and when it is momentarily at its lowest point during an oscillation.
(b) Explain qualitatively why the time required for one complete oscillation is the same in the spacecraft as it is in the laboratory, even though the gravitational field strengths differ drastically. In your explanation, identify the role that any constant background force plays in simple harmonic motion.
(c) State one assumption about the motion that must be satisfied in both environments for the conclusion in part (b) to remain valid.