Quick Start (Students)
Use presets and watch how position, velocity, and energy change.
- Press Run with “Spring: A=0.1, f=1” and relate the animation to x(t), v(t).
- Mark when v(t)=0 and point out turnarounds in the animation.
- Change A: the period stays the same, peaks get taller (E ∝ A²).
Teacher Tips
Prompt predictions, then validate with the graphs and calculators.
- Spring: double k or m; use chips (T, ω, f₀) to predict the new period.
- Pendulum (small): vary L and estimate T from T≈2π√(L/g); mass cancels.
- Use Phase to show v leads x by ~90°; damping spirals inward.
Common Misconceptions
Amplitude ≠ period; small‑angle pendulum period doesn’t depend on mass.
- Double A: period stays fixed; energy E grows (~A²); v(t) peaks increase.
- Pendulum mass change: no period change; only L and g matter (small angle).
Damping & Driving
Damping shrinks amplitude and total energy (Energy tab) and produces inward spirals in Phase. A periodic drive sustains motion; near resonance amplitude grows and phase shifts toward 90°.
Estimating f₀ fast
Spring: f₀=(1/2π)√(k/m). Pendulum (small): f₀≈(1/2π)√(g/L). Use the chips and the Derived Values card to verify against the x(t) plot.
Resonance Activity
Use Driven mode and vary fd around f₀. Sketch amplitude vs fd and discuss how damping reduces the peak and broadens the curve.
What is SHM?
Simple Harmonic Motion is motion under a restoring force proportional to displacement and directed toward equilibrium (F = −kx). The result is sinusoidal motion x(t)=A cos(ωt+φ), where ω depends on system parameters (e.g., ω=√(k/m) for a mass–spring, ω≈√(g/L) for a small‑angle pendulum). It conserves total mechanical energy in the ideal (undamped) case.