Topic: Oscillatory Motion
Concepts: Equivalence principle, Mass-spring system, Vertical spring

Solution:

Note that dropping the box changes the effective gravity experienced by the mass (in the box frame).

• A) Since the effective gravity $g$ changes, the equilibrium position and hence amplitude would change.
• B) The period is given by
  
  $T=2\pi\sqrt{\frac{m}{k}}$
  
  and is not affected by $g$.
• C) Since the amplitude changes, the maximum speed would change.
• D) Since the equilibrium position changes, the height where the mass reaches maximum speed would change.
• E) Since the amplitude changes, the maximum height reached by the mass would change.

Thus, the answer is B.