If the closed loop transfer function’s damping ratio is

If the closed loop transfer function’s damping ratio is 0.5 what is the value of M?

The C. E. = 4s² + s (M + 1) + 100 = 0

s² + s	M + 1	+ 25 = 0
	4

ω_n = √25 = 5
Given ξ = 0·5
<

2ξω_n =	M + 1
	4

2 × 0·5 × 5 =	M + 1
	4

5 × 4 = M + 1
M = 19