A marble is attached to a compressed horizontal spring and is then released. Which equation correctly shows the conservation of mechanical energy for this system

Question

Responses

1/2mv^2=kx^2

1/2mv^2=1/2kx^2

mgh=1/2kx^2

mgh=kx^2

Answer 1

The correct equation that shows the conservation of mechanical energy for a system where a marble is attached to a compressed horizontal spring and then released is:

1/2mv^2 = 1/2kx^2

This equation states that the kinetic energy (1/2 mv^2) of the marble when the spring returns to its equilibrium position is equal to the potential energy stored in the compressed spring (1/2 kx^2) when it is fully compressed.