Maximum acceleration in SHM

1 A particle \(P\), of mass 0.2 kg , moves in simple harmonic motion along a straight line under the action of a resultant force of magnitude \(F \mathrm {~N}\). The distance between the end-points of the motion is 0.6 m , and the period of the motion is 0.5 s . Find the greatest value of \(F\) during the motion.

A particle \(P\), of mass \(0.2\) kg, moves in simple harmonic motion along a straight line under the action of a resultant force of magnitude \(F\) N. The distance between the end-points of the motion is \(0.6\) m, and the period of the motion is \(0.5\) s. Find the greatest value of \(F\) during the motion. [5]

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-point of the cross-bar, both springs extend by 30 cm to the position \(A\), as shown. \includegraphics{figure_6} Each spring has natural length \(l\) m and modulus of elasticity \(\lambda\) N.

1. Show that \(\lambda = 392l\). [2 marks]

The 24 kg mass is left on the bar and the bar is then displaced downwards by a further 20 cm.

1. Prove that the system comprising the bar and the mass now performs simple harmonic motion with the centre of oscillation at the level \(A\). [5 marks]
2. Calculate the number of oscillations made per second in this motion. [3 marks]
3. Find the maximum acceleration which the mass experiences during the motion. [2 marks]