Can the Total Energy in a Spring Be Rearranged?

[JustinLiang]

Homework Statement

Since the total energy in a spring is
(1/2)kA^2

Can we rearrange this...
given k=F/x
(1/2)(FA^2/x)

Since x is also the amplitude, we have:
(1/2)(FA)
(1/2)(mgA)

I am pretty sure this is wrong, but why?

Thanks

 

[PhanthomJay]

Homework Statement

Since the total energy in a spring is
(1/2)kA^2

Can we rearrange this...
given k=F/x
(1/2)(FA^2/x)

Since x is also the amplitude, we have:
(1/2)(FA)

yes, where F is the max force in the spring and A is the absolute value of x.

(1/2)(mgA)

Only if F = mg, as when a mass is attached from a hanging spring and released.