How to use it
Press play and watch the marker travel along all four graphs at once — the point of the
activity is to see that every curve describes the same instant of the same motion.
- At maximum displacement the velocity is zero and the acceleration is largest and points back
towards equilibrium.
- Passing through equilibrium, displacement and acceleration are zero while the speed peaks.
- Tick a gradient box to draw the tangent at the current time: the gradient of the
displacement–time graph is the velocity, and the gradient of the
velocity–time graph is the acceleration. Compare the dashed box with the graph below it.
- Acceleration is always a = −ω2x, so the acceleration graph is
an upside-down copy of the displacement graph.
Open Change the system to vary length and gravity
(pendulum) or mass and spring constant (mass–spring) and see how the period responds. The
pendulum's drawn angle is capped so the picture stays sensible; the maths shown is always ideal SHM.
The horizontal axis
Horizontal axis re-labels every graph at once, so the three curves always stay lined
up. The motion itself never changes — only the way the axis is marked:
- Periods (T) — the default. Good for spotting that velocity peaks a quarter of a
cycle before displacement, whatever the period happens to be.
- Time / s — real seconds, so students can read a value straight off the axis.
Change the length or the mass and the same motion now spans a different number of seconds.
- Phase θ / rad and degrees — here θ = ωt is the
phase of the oscillation, not the angle of the pendulum string. One full cycle is
2π rad or 360°, which makes x = A cos θ easy to see.
Hiding a graph
Each graph has a Hide button. Hiding one leaves its space empty rather than closing the
gap, so the other graphs stay exactly where they were — useful for asking a class to sketch
the missing curve before revealing it.
The energy view
The fourth graph shows potential, kinetic and total energy on one axis, alongside the other
three so you can line an energy up against the displacement and velocity that produced it. Tick each
store off to show them in isolation.
- Total energy is a flat line: energy moves between the potential and kinetic stores, but the
sum never changes.
- Both energy curves repeat twice as often as the displacement graph, because energy depends on
x2 and v2 — the sign of the displacement makes no difference.
- The energy axis stays fixed when you change the system, so heavier masses or larger amplitudes
genuinely look bigger. Use Axis maximum to pick a scale that suits the numbers you are
working with; if the energy runs off the top, the graph says so.