A particle \(P\) of mass 0.25 kg is attached to one end of a light elastic string. The string has natural length 0.8 m and modulus of elasticity \(\lambda \mathrm { N }\). The other end of the string is attached to a fixed point \(A\). In its equilibrium position, \(P\) is 0.85 m vertically below \(A\).
Show that \(\lambda = 39.2\).
The particle is now displaced to a point \(B , 0.95 \mathrm {~m}\) vertically below \(A\), and released from rest.
Prove that, while the string remains stretched, \(P\) moves with simple harmonic motion of period \(\frac { \pi } { 7 } \mathrm {~s}\).
Calculate the speed of \(P\) at the instant when the string first becomes slack.
The particle first comes to instantaneous rest at the point \(C\).
Find, to 3 significant figures, the time taken for \(P\) to move from \(B\) to \(C\).