7.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{698b44b5-801c-45ec-b9de-021e44487edb-24_173_968_223_488}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{center}
\end{figure}

The fixed points $A$ and $B$ are 4 m apart on a smooth horizontal floor. One end of a light elastic string, of natural length 1.8 m and modulus of elasticity 45 N , is attached to a particle $P$ and the other end is attached to $A$. One end of another light elastic string, of natural length 1.2 m and modulus of elasticity 20 N , is attached to $P$ and the other end is attached to $B$. The particle $P$ rests in equilibrium at the point $O$, where $A O B$ is a straight line, as shown in Figure 6.
\begin{enumerate}[label=(\alph*)]
\item Show that $A O = 2.2 \mathrm {~m}$.

The point $C$ lies on the straight line $A O B$ with $A C = 2.7 \mathrm {~m}$. The mass of $P$ is 0.6 kg . The particle $P$ is held at $C$ and then released from rest.
\item Show that, while both strings are taut, $P$ moves with simple harmonic motion with centre $O$.

The point $D$ lies on the straight line $A O B$ with $A D = 1.8 \mathrm {~m}$. When $P$ reaches $D$ the string $P B$ breaks.
\item Find the time taken by $P$ to move directly from $C$ to $A$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M3 2017 Q7 [17]}}