MediumCalculusca-179

Damping Ratio from Overshoot

Problem

For a second-order underdamped system with percent overshoot Mp (as a fraction), the damping ratio is

zeta = -ln(Mp) / sqrt(pi^2 + ln(Mp)^2)

Given Mp in (0, 1), return zeta. A larger overshoot means a smaller damping ratio.

Hint

Mp = exp(-pi*zeta / sqrt(1 - zeta^2)) inverted gives this formula.

case 1

in: [0.5]

expected: 0.2154537619662468

case 2

in: [0.1]

expected: 0.5911550337988976

case 3

in: [0.25]

expected: 0.4037127519434207

case 4

in: [0.163]

expected: 0.5000425292061115

Starter codePython

def damping_from_overshoot(mp):
    # Your code here
    pass

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