A force of 3 N stretches a spring by 1 m. A mass of 4 kg is attached to the spring. At t=0 the
mass is pulled down a distance 1 m from equilibrium and released with a downward velocity of
0.5 m/s. Assuming that damping is negligible, determine an expression for the position of the
mass at time t. Find the circular frequency of the system and the amplitude, phase, and period of
the motion.

So... what do you have so far?

The basic differential equation for a mass, spring and damper is
my''+cy'+kx=0
but Since there is no damping, C= 0.

Any work with the given values?

Honestly, not really. F=kx
k=3y N/m.
4y''+3y=0 solving the ODE

I don't know if this is right?

Well, I really don't know how you do it in your syllabus, but that's what I would have done: Simple harmonic motion - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Simple_harmonic_motion#Dynamics_of_simple_harmonic _motion)

Or: x(t) = A \cos(\omega t - \phi)

Then proceed to find the things asked for.

Oh OK thanks. I'm working on it now