| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2002 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Time to travel between positions |
| Difficulty | Standard +0.3 This is a standard M3 SHM question requiring application of the velocity formula v² = ω²(a² - x²) to verify consistency and find parameters. Parts (a)-(c) involve routine substitution and algebraic manipulation, while part (d) requires integration of the standard SHM time formula, which is a bookwork technique. The multi-part structure and 13 marks indicate moderate length, but all steps follow established procedures without requiring novel insight or complex problem-solving. |
| Spec | 4.10f Simple harmonic motion: x'' = -omega^2 x |
The points $O$, $A$, $B$ and $C$ lie in a straight line, in that order, where $OA = 0.6$ m, $OB = 0.8$ m and $OC = 1.2$ m. A particle $P$, moving along this straight line, has a speed of $\left(\frac{1}{10}\sqrt{5}\right)$ m s$^{-1}$ at $A$, $\left(\frac{1}{5}\sqrt{5}\right)$ m s$^{-1}$ at $B$ and is instantaneously at rest at $C$.
\begin{enumerate}[label=(\alph*)]
\item Show that this information is consistent with $P$ performing simple harmonic motion with centre $O$. [5]
\end{enumerate}
Given that $P$ is performing simple harmonic motion with centre $O$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item show that the speed of $P$ at $O$ is 0.6 m s$^{-1}$, [2]
\item find the magnitude of the acceleration of $P$ as it passes $A$, [2]
\item find, to 3 significant figures, the time taken for $P$ to move directly from $A$ to $B$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2002 Q6 [13]}}