The tangential component of the gravitational force provides the restoring force: \(-mg \sin \theta = mL \frac{d^2\theta}{dt^2}\)
For small angles (\(\sin \theta \approx \theta\)): \(\frac{d^2 \theta}{dt^2} + \frac{g}{L} \theta = 0\)
This is a simple harmonic motion equation: \(\frac{d^2 \theta}{dt^2} + \omega^2 \theta = 0\) where \(\omega = \sqrt{\frac{g}{L}}\).
The general solution for the angular displacement \(\theta(t)\) is: \(\theta(t) = \theta_0 \cos\left( \sqrt{\frac{g}{L}} t + \phi \right)\) where:
The period \(T\) of the pendulum is the time for one complete cycle of oscillation: \(T = 2\pi \sqrt{\frac{L}{g}}\)
Myers famous introductory book to psychology contains 2 formulas and no symbolic exercises.
Goldstein’s famous introductory book to perception contains 4 formulas and no symbolic exercises.
Anderson’s famous introductory book to cognitive psychology contains 5 (relevant) formulas and 1 trivial symbolic exercise.
It is not a revolution in the sense of the “cognitive revolution” or of a Kuhnian paradigm shift (Kuhn, 1962) because it is not about the content of our science. Rather, it is about the values we hold as we conceptualize, implement, analyze, and share our science.”
Spellman (2015), p. 886