| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2014 |
| Session | June |
| Marks | 12 |
| Topic | Simple Harmonic Motion |
| Type | Maximum speed in SHM |
| Difficulty | Standard +0.3 This is a standard SHM problem with springs requiring equilibrium analysis, verification of SHM conditions, and calculation of standard parameters (amplitude, period, speed). While it involves multiple parts and careful bookkeeping of two equilibrium positions, each step follows routine procedures taught in mechanics courses. The conceptual demand is moderate—recognizing the new equilibrium and applying Hooke's law and SHM formulas—but no novel insight is required. |
| Spec | 4.10f Simple harmonic motion: x'' = -omega^2 x6.02e Calculate KE and PE: using formulae6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
One end of a light spring of length 0.5 m is attached to a fixed point $F$. A particle $P$ of mass 2.5 kg is attached to the other end of the spring and hangs in equilibrium 0.55 m below $F$. Another particle $Q$, of mass 1.5 kg, is attached to $P$, without moving it, and both particles are then released.
\begin{enumerate}[label=(\roman*)]
\item Show that the modulus of elasticity of the spring is 250 N. [2]
\item Prove that the motion is simple harmonic. [4]
\item Find
\begin{enumerate}[label=(\alph*)]
\item the amplitude of the motion, [1]
\item the greatest speed of the particles, [1]
\item the period of the motion, [1]
\item the time taken for the spring to be extended by 0.1 m for the first time. [3]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2014 Q10 [12]}}