Edexcel M3 2003 January — Question 4

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Year2003
SessionJanuary
TopicSimple Harmonic Motion

4. A piston \(P\) in a machine moves in a straight line with simple harmonic motion about a point \(O\), which is the centre of the oscillations. The period of the oscillations is \(\pi \mathrm { s }\). When \(P\) is 0.5 m from \(O\), its speed is \(2.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find
  1. the amplitude of the motion,
  2. the maximum speed of \(P\) during the motion,
  3. the maximum magnitude of the acceleration of \(P\) during the motion,
  4. the total time, in s to 2 decimal places, in each complete oscillation for which the speed of \(P\) is greater than \(2.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).