A horizontal spring, resting on a frictionless tabletop, is stretched 14 from its unstretched configuration and a 1.00- mass is attached to it. The system is released from rest. A fraction of a second later, the spring finds itself compressed 3.6 from its unstretched configuration.

Question

A horizontal spring, resting on a frictionless tabletop, is stretched 14  from its unstretched configuration and a 1.00- mass is attached to it. The system is released from rest. A fraction of a second later, the spring finds itself compressed 3.6  from its unstretched configuration.
How does its final potential energy compare to its initial potential energy? (Give your answer as a ratio, final to initial.)

drwls · Answer

You need stretch and mass dimensions after your numbers. However, in this case we can answer it anyway.

Potential Energy of a spring is proportional to the square of the stretch (or compression) dimension. 3.6 is 25.7% of 14. The P.E. will be (0.257)^2 = 6.6% of the original maximum-stretch value. The rest (93.4%) of the original energy becomes kinetic energy at that point