So I did this lab:

http://www.physics.ryerson.ca/sites/...pcs125/SHM.pdf
Essentially, we have a mass that was attached to a vertical spring with as little friction as possible. We let the mass reach equilibrium and then we applied a force on the mass. The mass oscillated with the same amplitude above and below the equilibrium position. We recorded the position of the mass and it looked like a perfect sine wave. My question is: what happens if we removed gravity? Also, we model simple harmonic motion and waves using sinusoidal functions. Can we model waves without these functions?