6. The figure shows a swing consisting of two identical vertical light springs attached symmetrically to a light horizontal cross-bar and supported from a strong fixed horizontal beam. When a mass of 24 kg is placed at the mid-
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point of the cross-bar, both springs extend by 30 cm to the position \(A\), as shown. Each spring has natural length \(l \mathrm {~m}\) and modulus of elasticity \(\lambda \mathrm { N }\).

1. Show that \(\lambda = 392 l\). The 24 kg mass is left on the bar and the bar is then displaced downwards by a further 20 cm .
2. Prove that the system comprising the bar and the mass now performs simple harmonic motion with the centre of oscillation at the level \(A\).
3. Calculate the number of oscillations made per second in this motion.
4. Find the maximum acceleration which the mass experiences during the motion.