Throughout the undergraduate course in Physics, the student frequently encounters problems involving oscillations. The primary model used to investigate oscillatory phenomena is the simple harmonic oscillator. As students advance in their academic education, they also learn various methods for solving differential equations. It is standard to employ such novel techniques in problems whose solution is previously known, to test the method’s quality and for didactic purposes. Placing these two lines together, I present twelve different ways to solve the well-known simple harmonic oscillator problem. They fall into three categories: basic, intermediate, and advanced. This division is based on the level of knowledge necessary to solve the problem, progressively acquired throughout the student’s academic education. Therefore, this material serves as a reference for students at distinct stages of their education.
Keywords:
Simple harmonic oscillator; Differential equation solutions.
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