Settling Time Estimate

Problem

For a second-order system with damping ratio zeta and natural frequency omega_n, the 2-percent settling time is commonly estimated as t_s = 4 / (zeta * omega_n).

Given zeta > 0 and omega_n > 0, return this estimate.

Hint

The envelope decays like e^(-zeta*omega_n*t); four time constants give 2 percent.

Test cases

case 1

in: [0.5,4]

expected: 2

case 2

in: [0.2,5]

expected: 4

case 3

in: [0.8,2]

expected: 2.5

case 4

in: [0.25,2]

expected: 8

Starter codePython

def settling_time(zeta, omega_n):
    # Your code here
    pass

4 test cases · run your code against them in the editor