| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2010 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Find period from given information |
| Difficulty | Standard +0.3 This is a straightforward application of standard SHM formulas (v² = ω²(a² - x²)) requiring substitution to find ω, then using standard results for maximum speed (aω) and maximum acceleration (aω²). All steps are routine with no problem-solving insight needed, making it slightly easier than average but still requiring correct formula recall and algebraic manipulation. |
| Spec | 6.05f Vertical circle: motion including free fall |
| Answer | Marks |
|---|---|
| 1 | Find period T using v 2 = ω2 (A 2 – x 2 ) and T = 2π/ω: ω = 6/4, T = 4π/3 or 4⋅19 [s] M1 A1 |
| Answer | Marks |
|---|---|
| (ii) Find mag. of max accel. using amax = ω2 A: amax = 45/4 or 11⋅2[5] [ms -2 ] M1 A1 | 2 |
| Answer | Marks |
|---|---|
| 2 | [6] |
Question 1:
1 | Find period T using v 2 = ω2 (A 2 – x 2 ) and T = 2π/ω: ω = 6/4, T = 4π/3 or 4⋅19 [s] M1 A1
(i) Find max speed using vmax = ωA: vmax = 15/2 or 7⋅5 [ms -1 ] M1 A1
(ii) Find mag. of max accel. using amax = ω2 A: amax = 45/4 or 11⋅2[5] [ms -2 ] M1 A1 | 2
2
2 | [6]A particle $P$ is describing simple harmonic motion of amplitude 5 m. Its speed is 6 m s$^{-1}$ when it is 3 m from the centre of the motion. Find, in terms of $\pi$, the period of the motion. [2]
Find also
\begin{enumerate}[label=(\roman*)]
\item the maximum speed of $P$, [2]
\item the magnitude of the maximum acceleration of $P$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE FP2 2010 Q1 [6]}}