← all cardsTopic 8 · Oscillations · Equations & the two systems
The two standard systems
Spring: stiffness and mass only — g does not appear (same period on the Moon). Pendulum: length and g only — mass does not appear, valid for small angles (sin θ ≈ θ).
spring: T = 2π√(m/k) · ω = √(k/m) · pendulum: T = 2π√(L/g) · ω = √(g/L)What this actually means
Spring: T = 2π√(m/k). Gravity is absent from the formula, so the period is identical on the Moon. Gravity only shifts where equilibrium sits, and SHM cares only about displacement FROM equilibrium.
Pendulum: T = 2π√(L/g). Mass is absent because the restoring force (a component of weight) and the inertia both scale with m, so m cancels exactly.
The pendulum result holds only for small angles, where sin θ ≈ θ makes the restoring force genuinely proportional to displacement.
The trap
Putting g in the spring period or m in the pendulum period — each formula excludes exactly one of them.
Prove it — watch it be true
- Drag the mass slider: the period does not move
- Switch gravity to the Moon: the swing visibly slows, T grows
- Compare measured T with 2π√(L/g) — the match is the formula