Simple Pendulum | Interactive Physics model

Interactive experiment

Mass m (kg) Length L (m)

Period T2.006 s

Frequency f0.498 Hz

Elapsed time0.000 s

Change mass or length, then start the pendulum.

Observation: Change the mass while keeping the length constant. The calculated period does not change. Now change the length and observe the effect on the period.

Simple Pendulum Python Simulation

This Python model calculates the period and frequency of a simple pendulum. Change the pendulum length or gravitational acceleration and compare the calculated results with the interactive simulation.

import math

# Simple pendulum experiment

mass = 1.0          # kg
length = 1.0        # m
g = 9.81            # m/s^2

# Small-angle pendulum period
period = 2 * math.pi * math.sqrt(length / g)

# Frequency
frequency = 1 / period

print("Mass =", mass, "kg")
print("Length =", length, "m")
print("Gravity =", g, "m/s^2")

print("Period =", round(period, 3), "s")
print("Frequency =", round(frequency, 3), "Hz")

# Notice:
# mass does NOT occur in the equation
#
# T = 2*pi*sqrt(L/g)
#
# Therefore, for an ideal simple pendulum,
# changing the mass does not change the period.

How Does a Simple Pendulum Work?

A simple pendulum consists of a mass suspended from a fixed point. For small oscillations, its period depends mainly on the pendulum length and gravitational acceleration. Increasing the length makes the pendulum take longer to complete each oscillation.

Pendulum Length and Period

Try changing the pendulum length in the simulation. Observe how the period and frequency change, and compare the experimental result with the theoretical prediction.

Challenge: Double the pendulum length from 1 m to 2 m. Predict whether the period will double. Then test your prediction using the simulator.