The governing equations for the springs and pendulums can be found at standard textbook or on the web (Have you try to search at wikipedia).
you will find SHM motion, if there is a small enough deviation from stable static equilibrium.
For example: touch the water surface lightly, knock the drum surface...

I guess it is your homework, so you should try to find out the answer by yourself. What you need is knowing what is SHM and looking at everything around you more carefully. And you will find many examples.