Circular Motion to Simple Harmonic Motion
Simple Harmonic Motion (SHM)—the back-and-forth oscillation seen in pendulums, springs, and waves—can be difficult to visualize mathematically. However, it is fundamentally just a one-dimensional projection of uniform circular motion. When you look at an object orbiting in a circle from the side, its shadow moves in perfect simple harmonic motion.
This interactive simulator allows you to visualize this geometric relationship in real time by projecting a 3D circular orbit onto a linear timeline to generate a classic sine wave.
How to use this simulator:
Simple Harmonic Motion (SHM)—the back-and-forth oscillation seen in pendulums, springs, and waves—can be difficult to visualize mathematically. However, it is fundamentally just a one-dimensional projection of uniform circular motion. When you look at an object orbiting in a circle from the side, its shadow moves in perfect simple harmonic motion.
This interactive simulator allows you to visualize this geometric relationship in real time by projecting a 3D circular orbit onto a linear timeline to generate a classic sine wave.
How to use this simulator:
- Adjust Phase Difference: Change the starting positions of two separate vectors to see how phase angles shift their corresponding waveforms
- Rotate the 3D View: Tilt and turn the spatial perspective to transition directly between seeing the full 2D circular orbit and its 1D linear shadow.
- Track Live Data: Monitor the angular displacement ($\theta$) and linear position ($x$) parameters as the simulation runs.
