I can't do this question about SHM

A particle of mass 1.5kg is hanging in equilibrium attached to the free end of an elastic spring of natural length 1.2m which is hanging vertically. The particle receives an impulse of 6Ns parallel to the spring.

a) Show that the subsequent motion is simple harmonic. I have no idea where to being with this one.

b) Given that the period of motion is $\displaystyle \

\frac{{2\pi }}{5}

\$ calculate the modulus of the spring and the amplitude of the motion. This part of the question I used $\displaystyle \

v^2 = \omega ^2 (A^2 - x^2 )

\$ to find that the amplitude A=0.8m, but then I can't find the modulus of the spring $\displaystyle \

\lambda

\$ because I don't know the extension, so I'm stuck :(

Any help would be greatly appreciated.