OCR MEI Further Mechanics B AS Specimen — Question 5

Exam BoardOCR MEI
ModuleFurther Mechanics B AS (Further Mechanics B AS)
SessionSpecimen
TopicSimple Harmonic Motion

  1. Find an expression for the stiffness of the spring, \(k \mathrm { Nm } ^ { - 1 }\), in terms of \(m , h\) and \(g\). The particle is pushed down a further distance from the equilibrium position and released from rest. At time \(t\) seconds, the displacement of the particle from the equilibrium position of the system is \(y \mathrm {~m}\) in the downward direction, as shown in Fig. 5.3. You are given that \(| y | \leq h\).
  2. Show that the motion of the particle is modelled by the differential equation \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} t ^ { 2 } } + \frac { g y } { h } = 0\).
  3. Find an expression for the period of the motion of the particle.
  4. Would the model for the motion of the particle be valid for large values of \(m\) ? Justify your answer.