13 Two light elastic strings each have one end attached to a particle \(B\) of mass \(3 c \mathrm {~kg}\), which rests on a smooth horizontal table.
The other ends of the strings are attached to the fixed points \(A\) and \(C\), which are 8 metres apart.
\(A B C\) is a horizontal line.
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String \(A B\) has a natural length of 4 metres and a stiffness of \(5 c\) newtons per metre.
String \(B C\) has a natural length of 1 metre and a stiffness of \(c\) newtons per metre.
The particle is pulled a distance of \(\frac { 1 } { 3 }\) metre from its equilibrium position towards \(A\), and released from rest.
13
- Show that the particle moves with simple harmonic motion.
13 - Find the speed of the particle when it is at a point \(P\), a distance \(\frac { 1 } { 4 }\) metre from the equilibrium position. Give your answer to two significant figures.
[0pt]
[4 marks]