Problem — Pendulum on the Space Station

Problem

On the International Space Station, in microgravity, a pendulum is hung from a bar. What happens if you pull it sideways and let it go? Discuss why, and what is needed to reconstruct a harmonic oscillation under those conditions.

Solution

The period of the pendulum is $T = 2\pi\sqrt{\ell/g}$ and it diverges as $g \to 0$: without a gravitational restoring force there is nothing to bring the mass back down. The pendulum therefore does not oscillate, it stays where you leave it (or continues in a straight line by inertia if you give it a push): $\ev{g \to 0 \Rightarrow \text{no oscillation}}$ To have harmonic motion in microgravity a restoring force that does not depend on $g$ is needed: a spring. The mass-spring system has $T = 2\pi\sqrt{\frac{m}{k}}$ which does not contain $g$ and works anywhere. Moral: springs oscillate even in space, pendulums do not.

Links

Topics: Oscillazioni e moto armonico Concepts: Pendolo semplice · Moto armonico semplice Skills: Analisi di casi limite e fantafisica Objects: Pendolo semplice