Answer:
A. when the mass has a displacement of zero
Explanation:
The velocity of a mass on a spring can be calculated by using the law of conservation of energy. In fact, the total energy of the mass-spring system is equal to the sum of the elastic potential energy (U) of the spring and the kinetic energy (K) of the mass:

where
k is the spring constant
x is the displacement of the mass with respect to the equilibrium position of the spring
m is the mass
v is the velocity of the mass
Since the total energy E must remain constant, we can notice the following:
- When the displacement is zero (x=0), the velocity must be maximum, because U=0 so K is maximum
- When the displacement is maximum, the velocity must be minimum (zero), because U is maximum and K=0
Based on these observations, we can conclude that the velocity of the mass is at its maximum value when the displacement is zero, so the correct option is A.
When an object does not move even on pushing , static frictional force acts on in opposite direction of the applied force to stop the object from moving. static frictional force is a self adjusting force and it adjust its value according to the applied force if the applied force is smaller than the maximum value of static frictional force. The object starts moving once the applied force on it becomes greater than the maximum static frictional force. hence the statement is true.