Using conservation of energy to find spring constant but off number

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SUMMARY

The discussion centers on calculating the spring constant for a .60 kg metal sphere oscillating on a vertical spring, with the spring stretching from .12 m to .23 m. The user initially calculated the spring constant as 114 N/m, while suggesting it should be 180 N/m. The calculations involve changes in gravitational potential energy and spring potential energy as the sphere's speed decreases from 5.7 m/s to 4.80 m/s during the spring's extension.

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slambert56
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Okay so I think the answer should be 180N/m unless the book is wrong and I got 114N/m. Now if there is a mistake in my work shown in the picture it would have to be the height final or height initial. I am going with height inital is the x initial and the height final equals the x final.(I think this is correct)

question; a .60kg metal sphere oscillates at the end of a vertical spring. as the spring stretches from .12 to .23m(relative to its unstrained length) the speed of the sphere decreases from 5.7 to 4.80m/s. what is the spring constant of the spring?
http://img231.imageshack.us/img231/8118/001ql.jpg

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sorry for the work on the back that you can see. any help would be greatly appreciated!
 
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As the spring stretches, the mass is at a lesser height, therefore has less gravitational potential energy, but more potential energy due to the spring.

You could consider the height to be -x.
 

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