A bucket of water and a mass-spring system are placed inside an elevator. A uniform wooden cylinder floats upright in the bucket of water. When displaced vertically, the cylinder bobs up and down with a period $T_b$. The mass on the spring oscillates vertically with a period $T_s$. Initially, the elevator is at rest. Then, the elevator accelerates upward with a constant acceleration $a = g$. Once the system reaches its new equilibrium, the cylinder and the mass are again slightly displaced so that they oscillate. What are the new periods of oscillation for the cylinder and the spring, respectively?