I'm doing a lab and I'm not sure I understand this concept. I've calculated the Spring Constant based on a plot of Force against Displacement to be 700.43. The spring is compressed 52mm, or .052 meters. If I use those vales for the formula 1/2 kx^2, I get (1/2)(700.43)(.052^2) = .947 as the Elastic Potential Energy.

My issue comes in when I calculate the kinetic energy of the same system. I'm getting around 450 for the entire system, which makes no sense if the potential energy doesn't match (this is a conservation of energy experiment.) Can someone explain what I am missing? If more detail is required, I'll be happy to add to my question. Thanks in advance.

I'm almost positive the constant is correct, it falls in the correct sample interval. So the kinetic energy... I made some really bad decimal mistakes, mainly on g-kg, but I corrected that and still come up short. So here:

The lab was to shoot a ball out of a spring cannon. The ball sits in a piston which is propelled by the compressed spring. The ball is 9.7g or .0097kg. velocity was calculated at 3.246m/s. Putting that in for Kinetic Energy, I get .051. Then we are given the masses for the piston and spring, 55.6g and 58/3g or 19.333...g, which using the same velocity gets me .293 and .102 respectively.

If that's the total kinetic energy at roughly .450, then it still doesn't match the potential energy of .947, plus the gravitational energy which makes the total closer to 1.000. I'd get it if it was off by 10%, I think it should be due to friction, but that wouldn't account for 55%, would it?