Equation #6: Simple Harmonic Motion
Every oscillating object can be approximated by an ordinary differential equation(given above), assuming the amplitude of oscillation stays small. In this case, there has to be a force acting on the object keeping it oscillating around a mean position.
For example, if you stretch a spring and let it go(one end of the spring remains fixed), it starts a cycle of compressing and stretching and compressing and stretching. This kind of oscillatory motion is very important in physics and helps us solve many seemingly complicated problems.
Watch a simple demo here: https://www.youtube.com/watch?v=_8PR6kaNUcQ
For more equations in Physics, see Famous equations in Physics