Pendulum Lab
Loading simulation…
flagWhat you'll discover
- arrow_forwardMeasure the period of a pendulum and compare it with the formula T = 2π√(L/g)
- arrow_forwardShow by experiment that the period depends on length and gravity — not on amplitude (for small swings) or mass
- arrow_forwardSee how damping slowly drains energy from an oscillator
- arrow_forwardRead an angle-time graph and recognise simple harmonic motion
What makes a pendulum swing?
Pull a pendulum bob to one side and gravity supplies a restoring force that always points back towards the lowest point. The bob accelerates towards the centre, overshoots, slows, and swings back — repeating forever if nothing steals its energy.
For small angles this restoring force is proportional to the displacement, which is the defining condition for simple harmonic motion (SHM). That is why a clock pendulum keeps such steady time: each swing takes the same duration regardless of how wide it is, a property called isochronism that Galileo first noticed in a swinging cathedral lamp.
The period formula
For small swings the time period is T = 2π√(L/g), where L is the length from pivot to the centre of the bob and g is the acceleration due to gravity. Notice what is missing: the mass of the bob and the amplitude do not appear at all.
Double the length and the period grows by √2, about 1.41 times. Move the same pendulum to the Moon, where g is 1.62 m/s² instead of 9.81 m/s², and each swing takes about 2.5 times longer. The simulation lets you verify both predictions with a stopwatch.
Damping and real pendulums
A real pendulum swings through air, and air resistance removes a little energy every swing. The amplitude decays gradually while — surprisingly — the period stays almost exactly the same. This is called damped oscillation.
Switch damping on in the simulation and watch the angle-time graph: the peaks shrink in a smooth exponential envelope, but the spacing between the peaks does not change. Clockmakers exploit this: they only need to top up the energy (with a spring or weights) and the timekeeping stays accurate.
Why large swings break the rule
The formula T = 2π√(L/g) comes from approximating sin θ ≈ θ, which is only accurate for small angles (below roughly 15°). Swing the pendulum from 60° or more and each oscillation takes measurably longer than the formula predicts.
The simulation solves the exact equation of motion, α = −(g/L)sin θ, so you can test this yourself: set a large initial angle and compare the measured period against the theoretical value in the readouts. The gap you see is real physics, not an error.