A pendulum that vibrates is one of a 'simple pendulum' or 'physical pendulum.' A simple pendulum is a case in which an object's angular motion can be ignored, such as a small object suspended from a string. Most pendulums are a 'physical pendulum' instead of a 'simple pendulum.'
Since Galileo's experiment, He found that the amplitude and the pendulum cycle are not related. This law only applies when the amplitude is tiny.
In practice, the pendulum cycle increases as the amplitude increases.