The positions of the moving objects were evaluated every 33 ms from a series of images and experimental results were compared with fundamental equations in mechanics to verify the technique. The motion of a free falling object and a simple pendulum were analyzed by digital cameras and computer programs (Sony Vegas, Adobe Photoshop and Microsoft Excel). In this paper, we attempt to apply this leaf function (or hyperbolic leaf function) to undamped pendulums and overdamped pendulums for large angles. The author has termed the function satisfying this differential equation the leaf function (or the hyperbolic leaf function). Curves based on solving this differential equation are constructed as regular waves with periods. The second derivative of a function is equal to the term multiplied by $-n$(or $n$) for terms whose function is raised to $2n-1$. On the other hand, the author has been studying a certain type differential equation. In cases where the angle of the pendulum is large, various methods have been presented that rely on numerical solutions and the exact solutions based on Jacobian elliptic functions, to name one example. Applying such linearization is limited to cases in which the angle of the pendulum is relatively small. To solve such problems, it is common to linearize the nonlinear equations and derive approximate numerical solutions and exact solutions. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. The mathematical model representing the equation of motion of a pendulum is nonlinear.

Square wave signal non linear pendulum