Introduction to simple harmonic motion

Equipment

• 3D phase circle with a uniformly rotating point and its displacement projection
• Sliders for amplitude A and frequency f
• Initial-phase slider φ
• Time plots of x, v, a and a Pause button

Procedure

1. Read the phase circle and displacement plot

   Run the simulation: the red point rotates uniformly on the circle, and its projection on the axis is the displacement $x = A\cos(\omega t + \varphi)$. Pause with the point at the top of the circle: the projection is at extreme, $v = 0$, and $a$ is maximal with opposite sign.

2. Vary A and f

   Raise amplitude A at fixed f: the x(t) curve grows taller, period unchanged. Raise f: the wave compresses, and $v_{\max} = A\omega$ grows with both. Check the $v_{\max}$ readout against $A\omega$ with $\omega = 2\pi f$.

3. Shift the initial phase

   Drag the φ slider: the whole x(t) trace slides in time while period and amplitude stay fixed — φ only sets the starting instant. Try φ = π/2: at t = 0 the body crosses equilibrium at maximum speed; predict the sign of v(0) before running.

Simulation

Experiment history

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