Standard +0.8 This M3 SHM question requires setting up and solving simultaneous equations using v² = ω²(a² - x²) for two positions, then finding the period. It involves algebraic manipulation of non-trivial equations and understanding of SHM theory beyond routine formula application, making it moderately challenging but within reach for well-prepared students.
A particle \(P\) moves with simple harmonic motion in a straight line, with the centre of motion at the point \(O\) on the line. \(A\) and \(B\) are on opposite sides of \(O\), with \(OA = 4\) m, \(OB = 6\) m.
When passing through \(A\) and \(B\), \(P\) has speed \(6\) ms\(^{-1}\) and \(4\) ms\(^{-1}\) respectively.
\includegraphics{figure_4}
\begin{enumerate}[label=(\alph*)]
\item Find the amplitude of the motion. [6 marks]
\item Show that the period of motion is \(2\pi\) s. [3 marks]
A particle $P$ moves with simple harmonic motion in a straight line, with the centre of motion at the point $O$ on the line. $A$ and $B$ are on opposite sides of $O$, with $OA = 4$ m, $OB = 6$ m.
When passing through $A$ and $B$, $P$ has speed $6$ ms$^{-1}$ and $4$ ms$^{-1}$ respectively.
\includegraphics{figure_4}
\begin{enumerate}[label=(\alph*)]
\item Find the amplitude of the motion. [6 marks]
\item Show that the period of motion is $2\pi$ s. [3 marks]
</end{enumerate}
\hfill \mbox{\textit{Edexcel M3 Q4 [9]}}