The Connection between Circular Motion and Simple Harmonic Motion

In this simulation, you can examine the connection between uniform circular motion and simple harmonic motion. This connection is one way to justify the basic equation of motion for an object experiencing simple harmonic motion. x = A cos (ωt) This equation also corresponds to one dimension of uniform circular motion. In this simulation, we even go beyond the equation above a little, and explore the phase angle, φ. In that case, the equation of motion becomes x = A cos (ωt + φ) There are analogous equations for the velocity and the acceleration as a function of time.