3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f07b8a65-ccb5-423f-96cc-b303bd05ad1f-05_495_972_239_484}
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\caption{Figure 2}
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Figure 2 shows a particle \(B\), of mass \(m\), attached to one end of a light elastic string. The other end of the string is attached to a fixed point \(A\), at a distance \(h\) vertically above a smooth horizontal table. The particle moves on the table in a horizontal circle with centre \(O\), where \(O\) is vertically below \(A\). The string makes a constant angle \(\theta\) with the downward vertical and \(B\) moves with constant angular speed \(\omega\) about \(O A\).
- Show that \(\omega ^ { 2 } \leqslant \frac { g } { h }\).
The elastic string has natural length \(h\) and modulus of elasticity \(2 m g\).
Given that \(\tan \theta = \frac { 3 } { 4 }\), - find \(\omega\) in terms of \(g\) and \(h\).