I am sorry, I was grossly wrong at the statement I made there. Thanks for pointing that out and correcting me. f(max) can never be equal to kx and will always be less than kx, otherwise the blocks wouldn't move at all as you rightly said.
Lets consider the FBDs of A and B separately,
suppose...
if kx exceeds μmg, there will be slipping and relative motion between the blocks. The frictional force at max displacement has to be less than μmg, only then the blocks will oscillate together without slipping.
Reason: The frictional force is STATIC and not DYNAMIC. Static friction adjusts...
(a) volume flow rate = (2.4/60) SI units
should be equal to (AREA*speed) = (50 cm^2)*speed = (0.25*speed) SI units
therefore speed = {2.4/(60*0.25} m/s
by LAW OF CONSERVATION OF VOLUME (MASS, assuming incompressible liquid)
(b) Now for calculating power, take density of water as 1000 Kg/m^3...
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