Answer
a) same
b) $t=0.0993~s$
Work Step by Step
(a) We know that the time period is independent of the initial speed of the block, hence the total time of contact is the same.
(b) We can find the required time as
$t=\frac{T}{4}$
$t=\frac{\pi}{2} \sqrt{\frac{m}{K}}$
We plug in the known values to obtain:
$t=\frac{\pi}{2} \sqrt{\frac{0.980}{245}}$
$t=0.0993~s$
