Does a spring oscillate at the same rate on the Moon as on Earth?

Yes. A mass on a spring has period T = 2π√(m/k), which depends only on the mass and the spring stiffness — gravity does not appear. A 1 kg mass on a 40 N/m spring has a period of 0.993 s on the Moon, on Mars, on Earth and on Jupiter alike. What gravity changes is the equilibrium stretch (4 cm on the Moon up to 62 cm on Jupiter), not the timing. This is the opposite of a pendulum, whose period T = 2π√(L/g) does depend on gravity — the same 1 m pendulum swings in 4.9 s on the Moon but 1.3 s on Jupiter.

How does adding mass change a spring’s stretch and period?

It changes them by different powers. The equilibrium stretch is x = mg/k, so it is proportional to mass — double the mass and the spring hangs twice as far (24.5 cm at 1 kg, 49.1 cm at 2 kg). But the period is T = 2π√(m/k), so it grows only as the square root of mass — doubling the mass lengthens the period by just √2, from 0.993 s to 1.405 s. Mass stretches the spring twice as fast as it slows the bob.

Where is the mass moving fastest, and where is the energy?

Released from the spring’s natural length, the mass moves fastest as it passes through the equilibrium point and is momentarily still at the two ends of its swing. The energy trades between elastic potential energy ½kx² and kinetic energy ½mv², and the two always add up to the same total ½kA² (1.203 J for the 1 kg / 40 N/m case). At equilibrium it is all kinetic — the peak speed here is 1.55 m/s; at the extremes it is all potential.

Motion

The Spring That Ignores Gravity

By Lucian — builder & engineer, LK Forge

Hang a mass on a spring and it settles, then, given a nudge, it bobs up and down at a steady beat. Two of the three things you might change — how heavy the mass is, how stiff the spring is, and how strong gravity is — set that beat. The third does nothing to it at all. Which one is the surprise, and it is exactly the one a pendulum cares about most. Worked out exactly from Hooke’s law, with the hanging-spring lab.

September 10, 2026 · 6 min read · exact from F = kx and T = 2π√(m/k)

0.993 s

spring period — the same on every planet

x ∝ m

double the mass, double the stretch

T ∝ √m

but only √2× the period

½kA²

total energy, constant through the swing

Same spring, four planets

Keep the mass and spring fixed and only change where you are standing. Gravity sets how far the spring hangs — that is Hooke’s balance k·x = m·g, so x = m·g/k grows straight with g. But the timing comes from how the spring pulls back once the mass is moving, k·x versus the mass’s inertia m, and gravity cancels clean out of that ratio. The last column is a 1 m pendulum in the same place, for contrast: it has no such immunity.

World	Gravity	Spring stretch	Spring period	1 m pendulum
Moon	1.62 m/s²	4 cm	0.993 s	4.937 s
Mars	3.72 m/s²	9.3 cm	0.993 s	3.258 s
Earth	9.81 m/s²	24.5 cm	0.993 s	2.006 s
Jupiter	24.79 m/s²	62 cm	0.993 s	1.262 s

m = 1 kg, k = 40 N/m. The spring period is frozen at 0.993 s while the stretch spans 15×; the pendulum period, by contrast, changes with every world. A spring-driven clock keeps time on the Moon; a pendulum clock runs almost 2.5× slow.

Mass pulls two levers at once

Adding mass does two things by two different rules, and confusing them is a classic trap. The stretch x = m·g/k rises linearly with mass; the period T = 2π√(m/k) rises with its square root. So over a four-fold range of mass the spring hangs four times farther but bobs only twice as slowly. Below, both are normalised to the 1 kg values so the two rates are directly comparable — the straight line is the stretch, the curve is the period.

Stretch (∝ m) outruns period (∝ √m): at 4 kg the spring hangs 4× as far but bobs only 2× as slowly. Stiffness works the other way — a stiffer spring both stretches less and bobs faster.

Energy sloshing back and forth

Release the mass and its energy pours between two forms: elastic potential ½kx² stored in the spring, and kinetic ½mv² in the moving mass. Each rises and falls, but their sum never changes — here it is fixed at 1.203 J for the 1 kg / 40 N/m spring. The mass is fastest (1.55 m/s) as it flies through equilibrium, where the energy is all kinetic, and momentarily frozen at each end, where it is all potential.

Potential and kinetic energy trade places twice a period; their sum is flat. Each peaks at the full 1.20 J the other hits zero.

Reproduce it yourself

Three formulas give every number on this page. Note what is — and is not — in each: gravity sets the stretch and the energy, but is nowhere in the period.

const m = 1, k = 40, g = 9.81;          // kg, N/m, m/s^2

const stretch = m * g / k;               // 0.245 m  (∝ g, ∝ m, ∝ 1/k)
const period  = 2 * Math.PI * Math.sqrt(m / k);  // 0.993 s  (no g!)
const energy  = 0.5 * k * stretch ** 2;  // 1.203 J  total ½kA²

// same spring on the Moon: stretch shrinks, period is unchanged
const stretchMoon = m * 1.62 / k;        // 0.040 m
const periodMoon  = 2 * Math.PI * Math.sqrt(m / k);  // 0.993 s — identical

These are lifted straight from the Hooke’s-law lab; the planet, mass and stiffness sweeps are the small script behind this post.

Stretch a spring

Open the lab, change the mass and stiffness, switch gravity to the Moon, and release it to watch the energy trade between spring and motion.

Open the Hooke’s-law lab →

Share this X Facebook Reddit