SimplePendulumExplo​rer

Calculates motion of a nonlinear pendulum and simulates laboratory measurements and analysis.

A common laboratory exercise in introductory physics entails observation of the motion of a simple pendulum using a photogate stationed at the stable equilibrium point. The student measures the period as a function of maximum angular displacement and attempts to examine the validity of the harmonic small angle approximation.

This Live Script calculates the exact solution for the motion of an ideal nonlinear pendulum released from rest for a range of initial angles and compares the results to those obtained by numerical integration of the equation of motion and to the harmonic approximation. It illustrates nonlinear fitting of simulated student data for period versus amplitude with exact and approximate models. The script may interest students and instructors of physics and engineering. Try this suggestions are included for further exploration.