In slush casting, a metallic core is used to create hollow castings. This process involves pouring molten metal into a mold and then "slushing" or rotating the mold to form a thin layer of metal. The metallic core helps in the creation of the hollow interior and provides structural support for the casting. The use of a sand, wooden, or no core would not provide the necessary structural integrity or hollow feature required in slush casting.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is: