Simple Pendulum

Investigate how the length of a pendulum and the strength of gravity affect its time period. Change one variable at a time and compare the results.

Pendulum simulation

Watch the bob swing from one side to the other.

Schematic animation. The string length is represented proportionally, not at actual scale.

Experiment controls

Adjust a value to observe the effect.

Pendulum length 1.00 m

0.25 m2.00 m

Gravitational acceleration 9.81 m/s²

1.0 m/s²20.0 m/s²

Starting angle 15°

5°30°

Simulation running.

Calculated time period2.01 s

Frequency0.50 Hz

Angular frequency3.13 rad/s

Oscillations per minute29.9

Theory and formula

For an ideal simple pendulum undergoing small oscillations, its time period depends on its length and the local gravitational acceleration.

T ≈ 2π√(L/g)

T = time period · L = length · g = gravitational acceleration

Frequency is the number of complete oscillations per second. For this approximation, changing the bob's mass does not change the calculated time period.

Experiment procedure

Set gravity to 9.81 m/s² and choose a length.
Record the calculated time period and frequency.
Change the length while keeping gravity constant. Compare the results.
Restore the original length and change gravity.
Try a different starting angle and observe the swing. The formula is an approximation, especially at larger angles.

Your observation table

Add each setting to the table and compare the calculated values. These are theoretical results, not physical measurements.

#	Length (m)	Gravity (m/s²)	Angle (°)	Period (s)	Frequency (Hz)
No observations recorded yet.

You can record up to 20 observations.

Model limitations: This simulation assumes a light, inextensible string, a point-like bob, and negligible air resistance and pivot friction. The displayed period uses the small-angle approximation; the animation illustrates the swing rather than solving the full nonlinear pendulum equation.