| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Difficulty | Standard +0.3 This is a straightforward application of standard SHM formulas with clearly stated initial conditions. Parts (a) and (b) require direct substitution into amplitude and acceleration formulas using the given period and initial velocity, while part (c) involves solving a simple trigonometric equation. All steps follow routine procedures covered in M3 with no novel problem-solving required. |
| Spec | 4.10f Simple harmonic motion: x'' = -omega^2 x |
A particle $P$ moves in a straight line with simple harmonic motion about a fixed centre $O$. The period of the motion is $\frac{\pi}{2}$ seconds. At time $t$ seconds the speed of $P$ is $v$ m s$^{-1}$. When $t = 0$, $P$ is at $O$ and $v = 6$. Find
\begin{enumerate}[label=(\alph*)]
\item the greatest distance of $P$ from $O$ during the motion, [3]
\item the greatest magnitude of the acceleration of $P$ during the motion, [2]
\item the smallest positive value of $t$ for which $P$ is 1 m from $O$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2012 Q2 [8]}}