A $0\mathrm{.}50-$kg disk is attached to a vertical spring $($spring constant $600$ N$/$m$)$ as shown on the figure. A $100-$g ball of clay is initially held at a point right above the disk, at a height of $1\mathrm{.}00$ m measured from the disk's surface. After the ball is released, it falls down, strikes the disk, and sticks to its surface. The ball and the disk oscillate up and down together. Calculate the amplitude of the oscillations