A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $$fA$$. The value of $$f$$ is:

A

$$\frac{1}{\sqrt{2}}$$

B

$$1$$

C

$$\frac{1}{2}$$

D

$$\sqrt{2}$$