In the process of physics competition learning, students will inevitably encounter the problem of small-quantity approximation. When to approximate and to what order often puzzles a large number of students, especially in the examination room. Reasonable approximation can bring twice the result with half the effort. This paper helps students determine the order of approximation and thus correctly solve such problems by using the principle of small quantity approximation in two semi-final questions.

Taking a simple pendulum as an example, this paper uses Gaussian AGM function and series expansion method to approximate the period of the pendulum, and compares it with theoretical values, It also cleverly solves the period problem of a pure rolling ball in a circular orbit.