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Vertical Spring Simple Harmonic Motion

Vertical Spring Simple Harmonic Motion
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2024-10-14 20:27
VectorFunctionParametric EquationSlider AnimationLocus
In collections The Domain of the Time (intuitive kinematics)
This GeoGebra applet demonstrates Simple Harmonic Motion (SHM) of a mass attached to a vertical spring. The construction uses Point, Circle, Segment, and CurveCartesian commands to build a spring-mass system simulating SHM. Key mathematical concepts include: SHM equation x(t)=A·cos(ωt+φ), period formula T=2π√(m/k), energy conservation, and mechanical oscillations. The applet features: displacement-time curves drawn with CurveCartesian, conditional logic with If, slider animations controlling time parameter t, and vector representations of velocity v and force F. Ideal for high school physics courses on mechanical vibrations, university mechanics lessons, or interdisciplinary teaching combining parametric equations with physical motion.

GeoGebra Commands & Parameters

  1. Point(Segment[(2 * O') - P', O']) → Q
  2. If(Length[reg] ≟ 1, {reg(1)}, Sequence[reg(k) - reg(k + 1), k, 1, Length[reg] - 1]) → regDif
  3. mean(regDif) → T
  4. Circle(M, r) → cir_{1}
  5. Segment((x(B) + 0.1, y(Q)), (x(B) + 0.1, y(O'))) → j
  6. Circle(M, abs(g)) → cir
  7. CurveCartesian((1.2 * sin(((20 * pi) * (t - (y(M) + 0.5)) / (y(P0) - (y(M) + 0.5))))), t, t, y(M), y(P0)) → muelle

AI Drawing Prompt Reference

Create a diagram of vertical spring simple harmonic motion: draw the spring geometry using a sinusoidal curve whose position is governed by an expression involving a time parameter, so the curve represents the displacement–time behavior. Place a mass point at the spring end and include circular markers to show reference amplitudes/length scales near the mass. Add a short vertical line segment connecting a reference point to the mass’s current height. Drive the time parameter with a slider so the spring/mass motion updates, and set the curve’s vertical extent using the heights of the mass point and another reference point, conveying oscillation through the evolving trajectory.
The prompt above was compiled from the original drawing commands and is for reference only.