| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2018 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Find period from given information |
| Difficulty | Standard +0.3 This is a standard M3 SHM question requiring application of the standard formulas v² = ω²(a² - x²) and a = -ω²x. Part (a) involves straightforward substitution to find ω then the period. Parts (b) and (c) require routine manipulation of SHM equations and basic trigonometry. While it's a multi-part question requiring several steps, all techniques are standard textbook exercises with no novel insight needed. |
| Spec | 4.10f Simple harmonic motion: x'' = -omega^2 x |
2. A particle $P$ is moving in a straight line with simple harmonic motion about the fixed point $O$ as centre. When $P$ is a distance 0.02 m from $O$, the speed of $P$ is $0.3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the magnitude of the acceleration of $P$ is $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
\begin{enumerate}[label=(\alph*)]
\item Find the period of the motion.
The amplitude of the motion is $a$ metres.
Find
\item the value of $a$,
\item the total length of time during each complete oscillation for which $P$ is within $\frac { 1 } { 2 } a$\\
metres of $O$. metres of $O$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2018 Q2 [11]}}