Conservation of energy spring problem

[whynot314]

Homework Statement

A block of mass m=2.00 kg is attached to a spring of force constant κ=500 N/M. the block is pulled to a position xi=.05m and released from rest. Find the speed the block has as it has passed equilibrium. Assume frictionless.

Homework Equations

ΔEsystem=ƩT(transfer)
Δk+ΔU=W

The Attempt at a Solution

I am assuming that this is a non isolated system.So I am having trouble setting up this equation I know work done by spring=1/2kX^2 and I know what Δk is, but Do I need to include the difference in elastic potential? I have seen this worked out without the elastic potential. why is it not included? and they just solved 1/2mv^2=1/2kx^2?

 

[Spinnor]

You know that when the mass vibrates and there is no friction the total energy of the system remains constant. The total energy E is,

E = 1/2mv^2 + 1/2kx^2 = constant = 1/2k(x_o)^2 where x_o is the initial amount the spring is stretched.

1/2mv^2 + 1/2kx^2 = 1/2k(x_o)^2 but we want to know v when x = 0 so,

1/2mv^2 = 1/2k(x_o)^2

So use the last equation you wrote but remember x is the initial amount the spring was stretched.