Why Do Different Methods Yield Different Spring Constants in Physics Problems?

[I love physics]

Homework Statement

A block of mass M is hung on a vertical spring.
We have to find spring constant k, x (displacement from mean position) given.

Homework Equations

1/2kx^2 = mgx
mg=kx

The Attempt at a Solution

When i conserve energy,
1/2kx^2=mgx
⇒ k= 2mg/x

But when i use mg=kx,
I get k=mg/x

But mg/x≠2mg/x,
Help please :)

 

[.Scott]

You don't need to compute energy here.
Just use Hooke Law directly.

What force is M applying to the spring?
How far is this causing the spring to stretch?

The assumption here is that the system is stable at x.

 

[I love physics]

You don't need to compute energy here.
Just use Hooke Law directly.

What for is M applying to the spring?
How far is this causing the spring to stretch?

The assumption here is that the system is stable at x.

after that it is given some velocity v from down, i need to calculate how high will it go.
i used 1/2kx²=1/2mv² is it correct?

 

[haruspex]

i used 1/2kx²=1/2mv² is it correct?

Is that based on some reasoning or just a wild guess?

If it rises above the equilibrium point by a maximum of h, what are the changes in

1. KE
2. GPE
3. Elastic PE

?

 

[J Hann]

Consider the situation of the mass moving horizontally along a frictionless surface.
What is the difference in the two situations?