State the meaning of simple harmonic motion.
A small ball is at rest at point $P$ on a curved track with radius $r$, as shown in Fig. 4.1. The ball is displaced a short distance to one side and then released. Its horizontal displacement $x$ is linked to its acceleration $a$ towards $P$ by $a = -\frac{gx}{r}$, where $g$ is the acceleration of free fall. Show that the ball undergoes simple harmonic motion.
The radius $r$ of curvature of the track is $28\,\text{cm}$. Determine the time interval $\tau$ between the ball passing point $P$ and then returning to point $P$.
A small ball is at rest at point P on a curved track with radius $r$, as shown in Fig. 4.1. The ball is displaced a short distance to one side and then released. Its horizontal displacement $x$ is linked to its acceleration $a$ towards P by $a = -\dfrac{gx}{r}$, where $g$ is the acceleration of free fall.
The graph in Fig. 4.2 shows how the displacement $x$ of the ball in (b) varies with time $t$. Moisture now appears on the track, so the ball stops after about $15$ oscillations. On the axes of Fig. 4.2, sketch how the displacement $x$ of the ball varies with time $t$ for the first two periods after the moisture has formed. Assume the moisture forms at time $t = 0$.