The correct equation that shows the conservation of mechanical energy for the system where a marble is attached to a compressed horizontal spring is:
\( \frac{1}{2} mv^2 = \frac{1}{2} k x^2 \)
This equation indicates that the kinetic energy of the marble (on release) is equal to the potential energy stored in the compressed spring at maximum compression. Thus, the correct response is:
12mv²=12kx² (1 half mv squared is equal to 1 half k x squared).