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As shown in the diagram, \(A\) and \(B\) are fixed points on a smooth horizontal table, where \(A B = 3 \mathrm {~m}\). A particle \(Q\) of mass 1.2 kg is attached to \(A\) by a light elastic string of natural length 1 m and modulus of elasticity \(180 \mathrm {~N} . Q\) is attached to \(B\) by a light elastic string of natural length 1.2 m and modulus of elasticity 360 N .
- Verify that when \(Q\) is in equilibrium \(B Q = 1.5 \mathrm {~m}\).
\(Q\) is projected towards \(B\) from the equilibrium position with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Subsequently \(Q\) oscillates with simple harmonic motion. - Show that the period of the motion is 0.314 s approximately.
- Show that \(u \leqslant 6\).
- Given that \(u = 6\), find the time taken for \(Q\) to move from the equilibrium position to a position 1.3 m from \(A\) for the first time.