A linear second-order system with the transfer functionG(s)

A linear second-order system with the transfer function
G(s) = 49
s² + 8s + 49

is initially at rest and is subject to a step input signal. The response of the system will exhibit a peak overshoot of—

We know that maximum overshoot is given as
M_p = e^{– ξπ}/√1 – ξ²

From given T.F. = G	49
	s² + 8s + 49

C.E. = s2 + 8s + 49
on comparing this equation with the standard equation
ωn^s + ω²_n = 0
2 ξω_n and ω_n = 7
or

ξ =	8	=	8	= .57
	2ω_n		2 × 7

% Mp = e	-3.14 × (0.57)²	× 100 = 2%
	√1 - (0.57)²

G(s) =	49
	s² + 8s + 49