7. A particle \(P\) of mass 2 kg is attached to one end of a light elastic string, of natural length 1 m and modulus of elasticity 98 N . The other end of the string is attached to a fixed point \(A\). When \(P\) hangs freely below \(A\) in equilibrium, \(P\) is at the point \(E , 1.2 \mathrm {~m}\) below \(A\). The particle is now pulled down to a point \(B\) which is 0.4 m vertically below \(E\) and released from rest.

1. Prove that, while the string is taut, \(P\) moves with simple harmonic motion about \(E\) with period \(\frac { 2 \pi } { 7 } \mathrm {~s}\).
2. Find the greatest magnitude of the acceleration of \(P\) while the string is taut.
3. Find the speed of \(P\) when the string first becomes slack.
4. Find, to 3 significant figures, the time taken, from release, for \(P\) to return to \(B\) for the first time.