State the meaning of simple harmonic motion.
A trolley of mass $m$ is supported on a horizontal surface by two springs. One spring is fixed to point $P$. The other spring is linked to an oscillator, as shown in Fig. 3.1. The springs, each with spring constant $k$ of $130\,\text{N m}^{-1}$, are always stretched. The oscillator is switched off. The trolley is displaced along the line of the springs and then released. The trolley then oscillates with simple harmonic motion. The trolley acceleration $a$ is given by $a = -\left(\frac{2k}{m}\right)x$, where $x$ is the displacement of the trolley from its equilibrium position. The trolley mass is $840\,\text{g}$. Calculate the frequency $f$ of oscillation of the trolley.
The oscillator in (b) is switched on. The frequency of oscillation of the oscillator is varied, while its amplitude of oscillation is kept constant. The trolley’s amplitude of oscillation is observed to change. The amplitude is greatest at the frequency calculated in (b). State the name of the effect responsible for this maximum.
At any given frequency, the trolley oscillates with a constant amplitude. Explain how this shows that resistive forces are acting against the motion of the trolley.