State two conditions that a mass must satisfy to be in simple harmonic motion.
A trolley of mass $950\text{ g}$ is supported on a horizontal surface by two springs fixed at points $P$ and $Q$, as shown in Fig. 4.1. Each spring has spring constant $k$ of $230\,\text{N m}^{-1}$, and both are always extended. The trolley is moved along the spring line and then let go. Fig. 4.2 shows how the displacement $x$ of the trolley varies with time $t$.
State and explain whether the trolley’s oscillations are heavily damped, critically damped or lightly damped.
Suggest what causes the damping.
The acceleration $a$ of the trolley of mass $m$ may be taken to be $a = -\left(\frac{2k}{m}\right)x$. Calculate the angular frequency $\omega$ of the trolley’s oscillations.
Determine the value of time $t_1$ indicated on Fig. 4.2.