| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2012 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Maximum speed in SHM |
| Difficulty | Standard +0.8 This is a multi-part M3 question requiring equilibrium analysis, energy conservation, SHM verification, and speed calculation. While the individual techniques are standard for Further Maths Mechanics, the question requires careful handling of elastic strings (distinguishing slack vs taut), energy methods, and SHM theory across multiple connected parts. The 14 total marks and need to integrate several concepts makes this moderately challenging, though not requiring novel insight. |
| Spec | 4.10f Simple harmonic motion: x'' = -omega^2 x6.02i Conservation of energy: mechanical energy principle |
A particle $B$ of mass 0.5 kg is attached to one end of a light elastic string of natural length 0.75 m and modulus of elasticity 24.5 N. The other end of the string is attached to a fixed point $A$. The particle is hanging in equilibrium at the point $E$, vertically below $A$.
\begin{enumerate}[label=(\alph*)]
\item Show that $AE = 0.9$ m. [3]
\end{enumerate}
The particle is held at $A$ and released from rest. The particle first comes to instantaneous rest at the point $C$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the distance $AC$. [5]
\item Show that while the string is taut, $B$ is moving with simple harmonic motion with centre $E$. [4]
\item Calculate the maximum speed of $B$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2012 Q7 [14]}}