Geometric Construction of SHM in a Horizontal Spring

This example demonstrates simple harmonic motion (SHM) of a horizontal spring by using a geometric construction that links the motion to a periodic projection. The displacement versus time exhibits a sinusoidal pattern with clear periodicity, illustrating how a spring’s SHM can be understood through phase, amplitude, and the cycle period. Key math concepts include the SHM model, relationships among period/frequency, sinusoidal displacement functions (sine/cosine form), and the geometric interpretation using rotating reference quantities. Construction-wise, it employs GeoGebra commands such as Point, If, Segment, Circle, and CurveCartesian to build the circle/radius structure and the time-dependent graph, while mean helps define reference or averaged quantities (e.g., equilibrium/baseline). Objects and parameters like amplitude, phase/time variables, period (T), time step (dt), velocity-related elements (v), and animation/control variables (e.g., slider-like parameters and restart/start logic) are organized to drive the motion and update visuals and labels. Suitable for high school to introductory college lessons on mathematical modeling, function graphs, and the geometric interpretation of SHM.