It may be called the simple pendulum but deriving the equation for its motion isn't easy.
The trick is to realise that, for the pendulum to continue swinging as it moves through the equililbrium position, the tension in the string is greater than the weight of the mass.
If a hanging ball is displaced to one side and released, it will swing backwards and forwards. This is because there is a restoring force that always points back towards the equilibrium position. If the swings are small, this force is proportional to the displacement, thus obeying simple harmonic motion.
Consider the forces acting on a pendulum bob. We can show that, for small swings, the acceleration is proportional to displacement and always directed towards the equilibrium position.
Use quizzes to practise application of theory.