The value of k for a unity feedback system with G(s) = k

The value of k for a unity feedback system with G(s) = k
s(1 + s)

to have a peak overshoot of 50% is _______

T(s) =	k
	s² + s + k

2 ξ ω_n = 1 , ω_n = √k

ξ =	0.5
	√k

M_p = 0.50 = exp		-π ξ
		√1 - ξ²

⇒	0.5	= 0.16
	√1 - ξ²

ξ = 0.15
k = 5.3

The value of k for a unity feedback system with G(s) =	k
	s(1 + s)