Calculating Elastic Potential Energy in a Vertical Spring System

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To calculate the elastic potential energy in a vertical spring system, the distance X must be determined as the stretch from the spring's equilibrium position. The elastic potential energy formula, PE = 1/2 K X^2, applies, where K is the spring constant. For the given object, the gravitational potential energy and translational kinetic energy can be calculated at different heights above the release point. The total mechanical energy remains constant throughout the motion, combining all forms of energy. Understanding the equilibrium position is crucial for accurately calculating the elastic potential energy.
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1.60 kg object is hanging from the end of a vertical spring. The spring constant is 48.0 N/m. The object is pulled 0.200 m downward and released from rest. Complete the table below by calculating the translational kinetic energy, the gravitational potential energy, the elastic potential energy, and the total mechanical energy E for each of the vertical positions indicated. The vertical positions h indicate distances above the point of release, where h = 0.

h (m)
0.0
0.200
0.400


ok..i got no problem with the translational kinetic energy, the gravitational potential energy and the total mechanical energy E...but I am confused about the elastic potential energy...i know its PE= 1/2KX^2
but how can i find X
 
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x would be the distance from the equiblrium position.
 
X = the distance the mass stretches the spring from the springs original position (no mass pulling on it)
 

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