What is the maximum kinetic energy of this vibrating mass?

Sometimes the quantities in physics can't be found from equations they're defined by, but we have to think about the physics in the background of the problem.
We might not have object's mass, but we do know that during the vibrating, a total kinetic energy of the object is converted into elastic potential energy of the spring and vice versa. The elastic potential energy PE = 1/2 x k x s², where s is the maximum strech of the spring, in our case, this is the amplitude s = 0.250 m. So, PE = KE = 0.5 x 20 N/m x (0.250 m)² = 0.625 J.

Maximum kinetic energy = (1/2)k*A^2
= (1/2) * 20 * 0.25^2
= 10 * 0.0625
= 0.625 J