Answer:
The compression is .
Explanation:
A Hooke's law spring compressed has a potential energy
where k is the spring constant and the distance to the equilibrium position.
A mass m moving at speed v has a kinetic energy
.
So, in the first part of the problem, the spring is compressed a distance d, and then launch the mass at velocity . Knowing that the energy is constant.
If we want to double the kinetic energy, then, the knew kinetic energy for a obtained by compressing the spring a distance D, implies:
But, in the left side we can use the previous equation to obtain:
And this is the compression we are looking for