Periodic motion parameters

Adjust amplitude, frequency, and phase to see how each parameter shapes the sinusoidal displacement. The oscillator and the graph share the same vertical scale — watch the dashed connector trace them in perfect sync.

Period
2.00s
Frequency
0.50Hz
Angular freq.
3.14rad/s
vmax = Aω
2.51m/s
amax = Aω²
7.90m/s²
Key equations x(t)  =  A cos(ωt + φ)      T  =  1/f  =  2π/ω      ω  =  2πf      vmax  =  Aω      amax  =  Aω²
Classroom ideas: Ask students why doubling f quadruples amax but only doubles vmax. Then change φ and ask: "The graph shifts — does the oscillator motion change, or only when it starts?"