Answer: let w be the angular frequency
For SHM w = (k / m)^1/2
w = 2 pi f = 2 pi / T = (k / m)^1/2
(T2 / T1)^2 = k1 / k2
or T2 / T1 = (1 / 2)^2 where x = - k x and k is the spring constant
if k is doubled then the period decreases by (1 / 2)^1/2
