When you push someone on a swing, they begin to oscillate back and forth.  Gravity is the "restoring force" that provides the repetitive cycles.  In the absence of any retarding forces, your friend would swing back and forth forever.	When you pull a mass down that is hanging from a spring and let it go, it begins to oscillate up and down.  The "restoring force" comes from the atomic interactions inside the spring.  In the absence of  retarding forces, the mass would bob up and down forever.
These two instances are STRIKINGLY similar!For each, the object has a fastest point in the middle of its travel, as well as end points where the velocity is zero (for a very short time).
Imagine that the person on the swing is dropping sand as they move.  If you could move a sheet sideways under them, what would you see?  A SINE WAVE	Imagine that the mass on the spring could leave marks on a paper that passed closely by.  What shape would you see?   A SINE WAVE
What is amazing here is that both of these situations are INTIMATELY related to circular motion.  Visit this site to see what I mean:  http://www.phy.ntnu.edu.tw/java/shm/shm.html