When the unit impulse response of a second order system is , the natural frequency and damping ratio of the system are respectively.

Concept:

The transfer function is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.

The closed-loop transfer function for the second-order system is:

Auxilliary Equation is given as:

s² + 2ξω_ns + ωn² = 0    ---(1)

ωn is the natural frequency of oscillations in rad/sec 

ξ  is the damping ratio

Calculation:

Impulse response h(t) as:

We know that:

A.E. is given as:

s² + 1.6s + 1 = 0

Comparing this with equation (1), we get:

ω_n² = 1

ω_n = 1

2ξω_n = 1.6

ξ = 0.8

Hence, option 1 is correct.