Problem $4.$ A nuclear reactor is critical and operates at a steady state at $P_{o}MW.$ Plot and discuss the reactor

power behavior as a function of time in the following cases. $(20$ points$)$

A$.$ Partial withdrawal of control rods from the reactor core with no reactivity feedback.

B$.$ Full insertion of control rods in the reactor core with no reactivity feedback.

C$.$ Partial withdrawal of control rods from the reactor core with positive reactivity feedback.

D$.$ Partial withdrawal of control rods from the reactor core with negative reactivity feedback.