For a frictionless
a. the maximum potential energy of the mass on a spring system occurs when the mass is positioned furthest from its equilibrium position.
b. the maximum kinetic energy of the system occurs when the mass is passing through the equilibrium position.

Both A and B is true

Explanation:

Given system is friction less

Consider a system of spring mass-system with general displacement equation

where A=maximum amplitude

=frequency of oscillation

Total Energy of the system is E=Potential Energy(U)+kinetic Energy(K)

At max amplitude

i.e.

where T = time period for one complete oscillation

at

thus and

i.e. Maximum at maximum amplitude

B.at mean position

i.e. total Energy is equal to Kinetic energy and Potential Energy is zero

hence B is true.