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