spring problem....?

Question

an 85 g wooden block is set up against a spring. The block rests on a smooth surface. The block is pushed into the spring, compressing it a distance of 2.0 cm and then released. The spring constant is k=78 N/m. What is the speed of the block when it reaches its initial position ( where the spring was not compressed)?

Answer 1

The initial energy of the system is spring potential energy, 1/2 k x^2 where x is the compression distance. When the block reaches the initial position the energy is entirely kinetic, 1/2 m v^2. So

1/2 k ( .02 m )^2 = 1/2 m v^2

Solve for the velocity v.