A system has a transfer function 

For a unit-step response and 2% tolerance band, the settling time will be

Concept:

The transfer function of the standard second-order system is:

ζ is the damping ratio

ωn is the natural frequency

Characteristic equation: 

Roots of the characteristic equation are: 

α is the damping factor

Settling time (Ts): It is the time taken by the response to reach ± 2% tolerance band as shown in the fig above.

  for a 5% tolerance band.

 for 2% tolerance band

Calculation:

By comparing the above transfer function with the standard second-order system,

⇒ 2ζωn = 1.6 ⇒ ζ = 0.4

As the damping ratio is less than unity, the system is underdamped.

Settling time,