Isocronism: Simple Harmonic Motion from Uniform Circular Motion

This example demonstrates isocronism by projecting uniform circular motion onto a line to obtain simple harmonic motion (SHM). It visually confirms that SHM has the same period as the generating circular motion when angular frequency is matched. Key concepts include the geometric correspondence between circular phase and SHM displacement, time-parameterized motion, and the period/frequency relationship that underlies the isocronism phenomenon. The construction uses GeoGebra elements such as Circle and Point to define the rotating reference, Angle to track the phase, Translate to shift reference positions, and CurveCartesian to draw the resulting oscillation curve from the projection. It also employs mean and Segment for establishing central references (e.g., midpoints/geometry scaffolding), plus animation/time objects to move points from t0 to t1 and compare the cycle structure. Suitable for high school through early undergraduate levels, especially for math-physics integration and interactive classroom demonstrations.