A block B of mass $$0.5\,\text{kg}$$ moving on a horizontal frictionless table at $$2.0\,\text{m s}^{-1}$$ collides with a massless pan P at origin O and sticks to it. The pan is connected at the end of a horizontal unstretched spring of force constant $$K=32\,\text{N m}^{-1}$$ as shown in the figure. After the block collides, the displacement of the block as a function of time $$t$$ is given by

A

$$0.25\cos 8t\,\text{m}$$

B

$$0.25\sin 8t\,\text{m}$$

C

$$2.50\sin\frac{t}{8}\,\text{m}$$

D

$$0.50\sin\frac{\pi t}{4}\,\text{m}$$