Pendulum period
01 // Question
How does the length of a pendulum's string change the time it takes to complete one swing?
One full swing out and back is called a period, written as T.
02 // Variables
Independent
Length of the pendulum string- 20 cm
- 40 cm
- 60 cm
- 80 cm
Dependent
Period of one full swing- Time for 10 swings, seconds
- Period T = time ÷ 10
03 // Hypothesis
IF the length of a pendulum's string increases, THEN its period will increase, BECAUSE a longer pendulum has farther to travel on each swing, and its period depends on the square root of its length.
04 // Procedure
1. Set the length
Measure the string from the pivot to the center of the mass, starting at 20 cm.
2. Pull to a small angle
Pull the mass back no more than about 15° from straight down.
3. Time 10 swings
Release and time how long it takes to complete 10 full swings, not just one.
4. Find the period
Divide the total time by 10 to get the period of one swing.
5. Repeat at each length
Repeat 3 trials at each length, then increase the length and repeat.
05 // Data table
| Length (cm) | Time for 10 swings (s) | Period T (s) | T² (s²) |
|---|---|---|---|
| 20 | ____ | ____ | ____ |
| 40 | ____ | ____ | ____ |
| 60 | ____ | ____ | ____ |
| 80 | ____ | ____ | ____ |
Formula T = 2π √(L ÷ g), where L is length in meters and g ≈ 9.8 m/s²
06 // What to expect
The period gets longer as the string gets longer, but not in a straight line — doubling the length does not double the period. Plotting T² against L instead of T against L straightens the curve into a line, because T² is directly proportional to L.
Changing the mass on the string barely changes the period at all, which usually surprises students expecting a heavier mass to swing slower.
07 // Lab notes
- Keep the release angle under about 15°. Beyond that, the simple pendulum formula stops being accurate.
- Time 10 swings instead of 1 — small timing errors on a single swing become a much bigger percentage of your result.
- Air resistance and friction at the pivot are the main real-world sources of error, and both slowly shrink the swing over time.
- Safety. Keep the pendulum stand steady during the lab — it is low hazard, but a falling stand can still pinch fingers.
08 // Remember
Mass doesn't matter. Only length and gravity decide the pendulum's rhythm.
09 // Questions people ask
Does the mass of the pendulum bob affect its period?
No, not in a simple pendulum. The period depends only on the string's length and the local strength of gravity — a heavier or lighter bob on the same length string swings at essentially the same rate.
Why time 10 swings instead of just 1?
Any small error in starting or stopping the stopwatch is the same size no matter how many swings you time, but it becomes a much smaller percentage of the total time when spread across 10 swings instead of 1.
What is the pendulum period formula?
T = 2π √(L ÷ g), where T is the period in seconds, L is the pendulum's length in meters, and g is the acceleration due to gravity, about 9.8 m/s² at Earth's surface.