Classical Mechanics: Simple harmonic oscillator problem

[JordanGo]

Homework Statement

A simple harmonic oscillator with mass m = 1/2 and k = 2 is initially at the point
x = √3 when it is projected towards the origin with speed 2.
Find the equation of motion describing x(t).

Homework Equations

x=Asin(ωt+θ)

The Attempt at a Solution

At t=0, x=√3

√3=Asin(θ)

There is two unknowns and only one equation...I'm stuck

 

[gomboc]

You just need to use a little ingenuity to solve for A.

You know that the mass is projected towards the eq point from x=sqrt(3) with velocity 2. Since you know the spring constant and the mass, you can find the mass's total energy, and thus it's position (A) at maximum extension using conservation of energy.

 

[technician]

Do you recognise that ω = √k/m ?

 

[JordanGo]

K, well I did a lot of work on white board and my conclusion is:
x(t)=2sin(4t-pi/3)
Does this make sense? Do you need to see all my work?