3 A fixed point A is 12 m vertically above a fixed point B. A light elastic string, with natural length 3 m and modulus of elasticity 1323 N , has one end attached to A and the other end attached to a particle P of mass 15 kg . Another light elastic string, with natural length 4.5 m and modulus of elasticity 1323 N , has one end attached to B and the other end attached to P .
- Verify that, in the equilibrium position, \(\mathrm { AP } = 5 \mathrm {~m}\).
The particle P now moves vertically, with both strings AP and BP remaining taut throughout the motion. The displacement of P above the equilibrium position is denoted by \(x \mathrm {~m}\) (see Fig. 3).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5bb02383-91c0-4454-aaea-0bd6af6ba325-4_405_360_751_849}
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\caption{Fig. 3}
\end{figure} - Show that the tension in the string AP is \(441 ( 2 - x ) \mathrm { N }\) and find the tension in the string BP .
- Show that the motion of P is simple harmonic, and state the period.
The minimum length of AP during the motion is 3.5 m .
- Find the maximum length of AP .
- Find the speed of P when \(\mathrm { AP } = 4.1 \mathrm {~m}\).
- Find the time taken for AP to increase from 3.5 m to 4.5 m .