Here is a formula for the solution of the undamped unforced oscillator
y''[t] + 25. y[t] = 0
You can damp this oscillator lightly by adding a modest damping term b y'[t]:
Your mission is to keep c as defined above and find the critical value bcritical so that if 0 < b < bcritical, then the oscillator y''[t] + b y'[t] + c y[t] = 0 is not overdamped (i.e. its solution formulas have sines and/or cosines), but if bcritical < b, then the oscillator y''[t] + b y'[t] + c y[t] = 0 is overdamped (i.e. its solution formulas have no sines or cosines).