| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2006 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Collision/impulse during SHM |
| Difficulty | Standard +0.3 This is a standard M3 SHM question requiring application of standard formulas (ω = 2πf, F_max = mω²a, v_max = ωa) with straightforward substitution. Part (b) adds a minor twist with doubled amplitude but uses the same formulas. The multi-step nature and need to connect frequency, amplitude, and force/velocity elevates it slightly above average, but it remains a textbook-style exercise without requiring novel insight or complex problem-solving. |
| Spec | 3.03d Newton's second law: 2D vectors4.10f Simple harmonic motion: x'' = -omega^2 x |
| Answer | Marks |
|---|---|
| \(a = 0.1\) | B1 |
| \(\frac{2\pi}{\omega} = \frac{1}{5} \Rightarrow \omega = 10\pi\) | M1 A1 |
| \(F_{\max} = ma\omega^2 = 0.2 \times 0.1 \times (10\pi)^2 \approx 19.7\) (N) | M1 A1 |
| (6) |
| Answer | Marks |
|---|---|
| \(a' = 0.2\), \(\omega' = 10\pi\) | B1ft, B1ft |
| \(v^2 = \omega'^2(a'^2 - x^2) = 100\pi^2(0.2^2 - 0.1^2) = (3\pi^2 \approx 29.6...)\) | M1 A1 |
| \(v \approx 5.44\) (m s\(^{-1}\)) | A1 |
| (5) | |
| Total: [11] |
**(a)**
| $a = 0.1$ | B1 |
| $\frac{2\pi}{\omega} = \frac{1}{5} \Rightarrow \omega = 10\pi$ | M1 A1 |
| $F_{\max} = ma\omega^2 = 0.2 \times 0.1 \times (10\pi)^2 \approx 19.7$ (N) | M1 A1 |
| | (6) |
**Note:** cao
**(b)**
| $a' = 0.2$, $\omega' = 10\pi$ | B1ft, B1ft |
| $v^2 = \omega'^2(a'^2 - x^2) = 100\pi^2(0.2^2 - 0.1^2) = (3\pi^2 \approx 29.6...)$ | M1 A1 |
| $v \approx 5.44$ (m s$^{-1}$) | A1 |
| | (5) |
| **Total:** [11] |
**Note:** If answers are given to more than 3 significant figures a maximum of one A mark is lost in the question.
---A particle $P$ of mass $0.2$ kg oscillates with simple harmonic motion between the points $A$ and $B$, coming to rest at both points. The distance $AB$ is $0.2$ m, and $P$ completes $5$ oscillations every second.
\begin{enumerate}[label=(\alph*)]
\item Find, to $3$ significant figures, the maximum resultant force exerted on $P$.
[6]
\end{enumerate}
When the particle is at $A$, it is struck a blow in the direction $BA$. The particle now oscillates with simple harmonic motion with the same frequency as previously but twice the amplitude.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find, to $3$ significant figures, the speed of the particle immediately after it has been struck.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2006 Q3 [11]}}