6. The diagram shows a playground ride consisting of a seat \(P\), of mass 12 kg , attached to a vertical spring, which is fixed to a horizontal board. When the ride is at rest with nobody on it, the compression of the spring is 0.05 m .
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The spring is of natural length 0.75 m and modulus of elasticity \(\lambda\).
- Find the value of \(\lambda\).
The seat \(P\) is now pushed vertically downwards a further 0.05 m and is then released from rest.
- Show that \(P\) makes Simple Harmonic oscillations of period \(\frac { \pi } { 7 }\) and write down the amplitude of the motion.
- Find the maximum speed of \(P\).
- Calculate the speed of \(P\) when it is at a distance 0.03 m from the equilibrium position.
- Find the distance of \(P\) from the equilibrium position 1.6 s after it is released.[3]
- State one modelling assumption you have made about the seat and one modelling assumption you have made about the spring.