Problem 5. Find the damping ratio and natural frequency of each of the following and determine whether the system is undamped, underdamped, overdamped or critically-damped. 5 T(s) = (s+3)(s+6) 10(s+7) T(s) (s + 10) (s+20) 20 T(s) = s² + 6s +144 s+2 T(s) = s² +9 T(s) = = = (s + 5) (s +10)²

Problem 5. Find the damping ratio and natural frequency of each of the following and determine whether the system is undamped, underdamped, overdamped or critically-damped. 5 T(s) = (s+3)(s+6) 10(s+7) T(s) (s + 10) (s+20) 20 T(s) = s² + 6s +144 s+2 T(s) = s² +9 T(s) = = = (s + 5) (s +10)²

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

Problem 5. Find the damping ratio and natural frequency of
each of the following and determine whether the system is
undamped, underdamped, overdamped or critically-damped.
5
T(s)
=
(s+3)(s+6)
T(s)
10(s + 7)
(s + 10) (s+20)
20
T(s) =
s² + 6s+ 144
s+2
T(s):
s² +9
T(s) =
=
=
=
=
(s+5)
(s+10)²

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