Answer:
The period would decrease by sqrt(2)
Explanation:
The restoring force is given by,
F = -kx
According to Newton's second law of motion,
ma = -kx
ma + kx = 0
The time period is given by,
T =
Where  is the angular velocity and it is given by,
 is the angular velocity and it is given by,
 =
 = 
Now if the spring constant is doubled then,

Thus,
 =
 =
 


Thus, The period would decrease by sqrt(2).
Hence, option D is correct.