The animation illustrates the relationship between circular motion and a harmonic wave. A rotating pointer in the circle generates a sinusoidal wave curve through its projection—a fundamental principle for understanding oscillations and waves.
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Description of the Animation
The animation shows how uniform circular motion and harmonic oscillation are mathematically related. A point moving at constant angular velocity on a circle generates a sinusoidal oscillation when projected onto an axis.
The rotating pointer (arrow) represents a vector of length A (amplitude) that rotates around the circle’s center. The instantaneous position of the pointer tip can be described by:
[ x = A cos(varphi) quad text{and} quad y = A sin(varphi) ]
The y-component of this circular motion corresponds exactly to the displacement of a harmonic wave. The green guide line connects the tip of the pointer with the corresponding point on the wave curve, making this relationship visible.
Interactive Controls
The animation provides two sliders for adjusting the wave parameters as well as a start/stop button:
- Wavelength: Determines the distance between two consecutive wave crests. A larger wavelength stretches the wave, a smaller one compresses it.
- Amplitude: Sets the maximum displacement of the wave. The radius of the circle adjusts automatically, as it corresponds to the amplitude.
- Start/Stop: Starts or pauses the animation. While running, the pointer rotates continuously and the green guide line moves along the wave curve.
Physical Background
This representation is fundamental for understanding alternating current, electromagnetic waves, and mechanical oscillations. Circular motion provides a clear geometric interpretation of the sine function and explains why terms such as “angular frequency” and “phase” are used in wave theory.