Projection of Simple Pendulum Motion

Angular position $\theta$ of simple pendulum, with bob mass $m$ and arm length $L$, relates to projection along horizontal direction

$$\tag{1} x = x_c + L \sin\theta$$

and vertical direction

$$\tag{2} y = y_c - L \cos\theta,$$

with positive direction of $\theta$ is in counter clockwise direction and $(x_c, y_c)$ is pivot position.

• -, “Trig and forces: the pendulum”, Khan Academy, 2022, url https://www.khanacademy.org/computing/computer-programming/programming-natural-simulations/programming-oscillations/a/trig-and-forces-the-pendulum [20221125].