State the meaning of simple harmonic motion.
A trolley with mass $m$ is supported on a horizontal surface by two springs. One spring is fixed to a stationary point $P$. The second spring is joined to an oscillator, as shown in Fig. 3.1. Each spring has spring constant $k$ of $130\,\text{N m}^{-1}$, and both springs remain extended at all times. The oscillator is turned off. The trolley is moved along the line of the springs and then let go. The trolley then performs simple harmonic oscillations. Its acceleration $a$ is described by $a = -\left(\frac{2k}{m}\right)x$, where $x$ is the displacement from equilibrium. The trolley has mass $840\,\text{g}$. Calculate the frequency $f$ of the trolley's oscillation.
The oscillator in (b) is switched on. Its frequency of oscillation is changed while its amplitude of oscillation is kept constant. The amplitude of oscillation of the trolley is observed to change. The amplitude reaches a maximum at the frequency calculated in (b). State the name of the effect that causes this maximum.
At a fixed frequency, the trolley's amplitude of oscillation remains constant. Explain how this shows that resistive forces are acting against the trolley's motion.