The simple pendulum — what determines its period?
What we'll do: We'll release two pendulums of different mass but the same length and check which one returns sooner — then we'll see what really changes the rhythm.
What you see on screen: Two pendulums swinging side by side (the larger bob = greater mass), sliders for length, mass and amplitude, plus an Earth / Moon toggle. The period bar shows that changing the mass does nothing, while changing the length does. Readouts: length, mass, amplitude, g and the period T.
What just happened?
Both pendulums — with the heavy and the light bob — returned at the same moment. Mass did not matter. The rhythm changed only when you changed the length.
Why does mass not matter?
The heavy bob is pulled down harder (greater force), but it is also more inert — harder to accelerate. These effects cancel exactly. The restoring force is
and the acceleration:
The mass cancelled out — only is left. That is why the rhythm of each bob is the same. Same principle as in free fall: without air resistance, a feather and a ball fall together.
So what does the period depend on?
Only the length and the gravitational acceleration . A longer pendulum → a longer period (slower). Under the square root: for the period to double, the length must quadruple. A smaller (Moon) → slower swinging.
And the amplitude?
For small angles it does not matter either — from a larger angle the path is longer, but the motion is faster, and the return takes the same time. This is isochronism (Galileo).
Why you need this for the exam:
The pendulum is a model of harmonic motion. From the formula you can determine — you measure and and rearrange the formula. A classic experimental task.
Remember: the pendulum's rhythm is set by length, not weight. That is why a pendulum clock is adjusted by sliding the weight (changing the length), not by adding mass.
Theory & formulas
Period of the simple pendulum
For small displacements: The period depends only on the length and the acceleration — not on mass nor (for small angles) amplitude.
Why mass has no effect
In the equation of motion the larger gravitational force () is balanced by larger inertia () — the mass cancels out.
Determining g
By measuring and :
Notation: — period, — pendulum length, — gravitational acceleration.
Frequently asked questions
›What determines the period of a simple pendulum?
Only on the length L and the acceleration g: T = 2π√(L/g) — not on mass nor (for small angles) on amplitude.
›Why does mass not affect the pendulum's period?
The larger gravitational force is balanced by larger inertia — the mass cancels out in the equation of motion.
›How do you determine g with a pendulum?
By measuring the length L and the period T, then rearranging the formula: g = 4π²L / T².
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