AS 91524 · 2024 paper · simple harmonic motion (watch glass)

Question 3(a) Achieved

A ball bearing is released on a watch glass — a shallow semi-circular glass bowl of radius of curvature R — and rolls back and forth with simple harmonic motion.

released 0.0400 m from equilibrium
T	0.882 s

State the two conditions for a ball rolling on a watch glass to show SHM.

The 2024 paper, page 6 ↗ Marking schedule, page 5 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1 As the ball moves further from the middle, what must happen to the force bringing it back?
It must grow in step: the restoring force, and so the acceleration, is proportional to how far the ball is from equilibrium (its displacement).
2 Which way must that force point?
Always back towards the equilibrium position, opposite to the displacement. Both conditions together: a = −ω²y.

Answer The restoring force (so the acceleration) is proportional to the ball’s displacement from equilibrium, and it always points back towards equilibrium, opposite to the displacement: a = −ω²y.

What the marker wanted

Achieved Both conditions, or the equation.

In our words, from NZQA’s 2024 marking schedule.

How did it go?

Got it moves it further out. Review brings it back tomorrow.