Question

Problem The response of an underdamped second order system to a step input can be expressed as S lf the espenmentally observed damped period of oscillation of the system is 0577ms and, from a logarithmic decrement analysis, the damping ratio is found to be 0.8, what is the damped circular frequency of the system? the natural frequency of the system

Answer 1

Damped Frequency:

$\small w_d = \frac{2\pi}{T}$

T = 0.577 ms

$\small w_d = \frac{2\pi}{0.577}$

$\small w_d = 10.889 rad/s$

Natural Frequency:

$\small w_d = w_n \sqrt(1- \zeta^2)$

$\small \zeta = 0.8$

$\small 10.889 = w_n \sqrt(1- 0.8^2)$

$\small w_n = 18.1483 rad/s$