| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2014 |
| Session | November |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Maximum speed in SHM |
| Difficulty | Challenging +1.2 This is a standard Further Maths mechanics question on SHM with elastic strings. Part (i) requires equilibrium force balance (routine). Part (ii) involves showing SHM by verifying F = -kx (standard technique for Further Maths). Part (iii) uses energy conservation. While it requires multiple steps and careful bookkeeping of extensions, the methods are all standard textbook procedures for FP2 SHM with no novel insight required. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05f Vertical circle: motion including free fall |
The points $A$ and $B$ are on a smooth horizontal table at a distance $8a$ apart. A particle $P$ of mass $m$ lies on the table on the line $AB$, between $A$ and $B$. The particle is attached to $A$ by a light elastic string of natural length $3a$ and modulus of elasticity $6mg$, and to $B$ by a light elastic string of natural length $2a$ and modulus of elasticity $mg$. In equilibrium, $P$ is at the point $O$ on $AB$.
\begin{enumerate}[label=(\roman*)]
\item Show that $AO = 3.6a$. [4]
\end{enumerate}
The particle is released from rest at the point $C$ on $AB$, between $A$ and $B$, where $AC = 3.4a$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Show that $P$ moves in simple harmonic motion and state the period. [6]
\item Find the greatest speed of $P$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE FP2 2014 Q5 [12]}}