| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2007 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Maximum speed in SHM |
| Difficulty | Moderate -0.5 This is a straightforward application of standard SHM formulas (v_max = ωa and v² = ω²(a² - x²)) with given values. Requires recall of formulas and basic substitution/algebra, but no problem-solving insight or complex manipulation, making it slightly easier than average. |
| Spec | 4.10f Simple harmonic motion: x'' = -omega^2 x |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \([\omega = 2\pi/6.1 = 1.03]\) | M1 | For using \(T = 2\pi/\omega\) |
| M1 | For using \(v_{max} = a\omega\) | |
| Speed is \(3.09 \text{ ms}^{-1}\) | A1 | [3 marks total] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For using \(v^2 = \omega^2(A^2 - x^2)\) or for using \(v = A\omega\cos\omega t\) and \(x = A\sin\omega t\) | |
| \(2.5^2 = 1.03^2(3^2 - x^2)\) or \(x = 3\sin(1.03 \times 0.60996...)\) | A1ft | ft incorrect \(\omega\) |
| Distance is 1.76m | A1 | [3 marks total] |
# Question 1:
## Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[\omega = 2\pi/6.1 = 1.03]$ | M1 | For using $T = 2\pi/\omega$ |
| | M1 | For using $v_{max} = a\omega$ |
| Speed is $3.09 \text{ ms}^{-1}$ | A1 | [3 marks total] |
## Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For using $v^2 = \omega^2(A^2 - x^2)$ or for using $v = A\omega\cos\omega t$ and $x = A\sin\omega t$ |
| $2.5^2 = 1.03^2(3^2 - x^2)$ or $x = 3\sin(1.03 \times 0.60996...)$ | A1ft | ft incorrect $\omega$ |
| Distance is 1.76m | A1 | [3 marks total] |
---1 A particle $P$ is moving with simple harmonic motion in a straight line. The period is 6.1 s and the amplitude is 3 m . Calculate, in either order,\\
(i) the maximum speed of $P$,\\
(ii) the distance of $P$ from the centre of motion when $P$ has speed $2.5 \mathrm {~ms} ^ { - 1 }$.
\hfill \mbox{\textit{OCR M3 2007 Q1 [6]}}