Hey!

amplitude =10 cm = 10^-1m

The object will not detached from the platform it angular frequency Wmax is such that during downward motion, the maximum acceleration equals to the acceleration due to gravity.

i.e. W^2max(A) =g

Wmax= sqrt(g/A)

Tmin=(2π/wmax) =2π sqrt(A/g)

A=10^-1m

g=10m/s2

Tmin=2π sqrt(10^-1/10)=2π(1/100)= 0.0628sec

Hope it helps!