$A$ block of mass $m$ starts at rest at height $h$ on a frictionless inclined plane. The block slides down the plane,travels across a rough horizontal surface with coefficient of kinetic friction $\mu$,and compresses a spring with force constant $k$ a distance $x$ before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface,sliding up the plane. The block travels a total distance $d$ on the rough horizontal surface. The correct expression for the maximum height $h'$ that the block reaches on its return is

• A
  $mgh' = mgh - \mu mgd$
• B
  $mgh' = mgh + \mu mgd$
• C
  $mgh' = mgh + \mu mgd + kx^2$
• D
  $mgh' = mgh - \mu mgd - kx^2$