| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Simple Harmonic Motion |
| Type | Displacement and velocity at given time |
| Difficulty | Standard +0.3 This is a straightforward SHM question requiring students to recognize the setup (amplitude = 0.1m, period = 0.4s), sketch a cosine curve shifted appropriately, and evaluate position at a given time using standard SHM formulas. While it's Further Maths content, the question involves direct application of standard techniques with no novel problem-solving or complex reasoning required, making it slightly easier than average. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities4.10f Simple harmonic motion: x'' = -omega^2 x |
$A$ is a fixed point on a smooth horizontal surface. A particle $P$ is initially held at $A$ and released from rest.
It subsequently performs simple harmonic motion in a straight line on the surface. After its release it is next at rest after $0.2$ seconds at point $B$ whose displacement is $0.2$ m from $A$. The point $M$ is halfway between $A$ and $B$.
The displacement of $P$ from $M$ at time $t$ seconds after release is denoted by $x$ m.
\begin{enumerate}[label=(\alph*)]
\item Sketch a graph of $x$ against $t$ for $0 \leq t \leq 0.4$. [4]
\item Find the displacement of $P$ from $M$ at $0.75$ seconds after release. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 2 2021 Q3 [6]}}