# Calculate energy of vertical oscillating spring

Problem statement:

An oscillating mass is hung from a vertical spring. Take the potential energy of the system when the spring is at the unstretched length to be zero for both spring and gravity. Calculate the gravitational potential energy, spring potential energy, and total potential energy of the system at:

Equilibrium
y cm above equilibrium
y cm below equilibrium

(Assume the spring can compress more than y and that F = -kΔx still holds)

Relative equations:
GPE = mgh
SPE = ½ k x^2

Work so far:

Equilibrium GPE = mgh
Equilibrium SPE = ½kh^2
Equilibrium TE = mgh + ½kh^2

y cm above GPE = mg(h-y)
y cm above SPE = ½k(h-y)
y cm above TE = mg(h-y) + ½k(h-y)

y cm below GPE = mg(h+y)
y cm below SPE = ½k(h+y)
y cm below TE = mg(h+y) + ½k(h+y)

haruspex
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Calculate the gravitational potential energy, spring potential energy, and total potential energy
In terms of what? You must be told what variables to express it in terms of, such as mass, spring constant, etc.

I'm afraid that is all the info the problem states. Let's assume m = mass, k = spring constant, h = amplitude, x_0 = position of mass at equilibrium. I was going to ask my instructor more about it at school tomorrow but I wanted to get a jump on the problem by making my own variables.