The correct option is (c) T1 = T2 = 2π √(m/k)

Explanation: For the spring mass system on the horizontal surface, F = -kx.

So, T1 = 2π/w = 2π √(m/k). When the spring mass system is hung from the ceiling, at mean position mg = kx0. Let spring be pulled further by x, extension = x+x0, F = k(x+x0)-mg

= kx + kx0– mg = kx. The force is proportional to x. Thus, w = √(k/m) & T2 = 2π √(m/k). Therefore, T1 = T2 = 2π √(m/k).