14 A particle, \(P\), of mass \(M\) is released from rest and moves along a horizontal straight line through a point \(O\). When \(P\) is at a displacement of \(x\) metres from \(O\), moving with a speed \(v \mathrm {~ms} ^ { - 1 }\), a force of magnitude \(| 8 M x |\) acts on the particle directed towards \(O\). A resistive force, of magnitude \(4 M v\), also acts on \(P\).
14
- Initially \(P\) is held at rest at a displacement of 1 metre from \(O\). Describe completely the motion of \(P\) after it is released.
Fully justify your answer.
[0pt]
[8 marks]
14 - It is decided to alter the resistive force so that the motion of \(P\) is critically damped.
Determine the magnitude of the resistive force that will produce critically damped motion.
[0pt]
[4 marks]