Pendulum Period

The Simple Pendulum

A mass on a string of length $L$ , swinging under gravity, oscillates with period:

$T = 2\pi\sqrt{\frac{L}{g}}$

where $g = 9.81$ m/s².

Historical Importance

Galileo noticed that pendulum period is independent of amplitude (for small angles). This led to pendulum clocks — the most accurate timekeepers for 300 years, from Huygens (1656) to quartz oscillators (1920s).

The Small-Angle Approximation

This formula holds when the angle is small ( $\lesssim 15°$ ). For large angles, the true period is longer and requires an elliptic integral to compute exactly.

Period vs Spring-Mass

	Spring-Mass	Pendulum
Formula	$2\pi\sqrt{m/k}$	$2\pi\sqrt{L/g}$
Restoring force	Spring: $F = kx$	Gravity: $F \approx mg\theta$
Effective "k"	$k$	$mg/L$

For the pendulum, the "spring constant" is $mg/L$ — so mass cancels out and period is mass-independent.

Examples

$L$ (m)	$T$ (s)
1.000	2.0061
4.000	4.0122
9.810	6.2832 $= 2\pi$
0.248	0.9990 $\approx 1$ s (a seconds pendulum)

Your Task

Implement pendulumPeriod(L) returning the period in seconds.

← Previous Next →

TCC compiler loading...

Click "Run" to execute your code.