| Exam Board | Edexcel |
|---|---|
| Module | FM2 (Further Mechanics 2) |
| Year | 2024 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Find amplitude from speed conditions |
| Difficulty | Standard +0.8 This is a multi-part SHM question requiring knowledge of the standard equations (v² = ω²(a² - x²) and max acceleration = ω²a), algebraic manipulation to find amplitude, and integration/inverse trig for part (c). While the techniques are standard for FM2, the question requires careful application across three parts with the final part being non-routine, placing it moderately above average difficulty. |
| Spec | 4.10f Simple harmonic motion: x'' = -omega^2 x |
| Answer | Marks | Guidance |
|---|---|---|
| \(\omega^2 a = 18\) | B1 | 3.4 |
| Use \(v^2 = \omega^2(a^2 - x^2)\) | M1 | 3.4 |
## 5(a)
$\omega^2 a = 18$ | B1 | 3.4
Use $v^2 = \omega^2(a^2 - x^2)$ | M1 | 3.4
$2.4^2\begin{enumerate}
\item A particle $P$ moves in a straight line with simple harmonic motion about a fixed point $O$. The magnitude of the greatest acceleration of $P$ is $18 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
\end{enumerate}
When $P$ is 0.3 m from $O$, the speed of $P$ is $2.4 \mathrm {~ms} ^ { - 1 }$\\
The amplitude of the motion is $a$ metres.\\
(a) Show that $a = 0.5$\\
(b) Find the greatest speed of $P$.
During one oscillation, the speed of $P$ is at least $2 \mathrm {~ms} ^ { - 1 }$ for $S$ seconds.\\
(c) Find the value of $S$.
\hfill \mbox{\textit{Edexcel FM2 2024 Q5 [11]}}