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(a) the system is underdamped with ξ = 0.09, (b) the system is critically damped; and (c) the system is over-damped with ξ = 1.2

(a) the system is underdamped with ξ = 0.09, (b) the system is critically damped; and (c) the system is over-damped with ξ = 1.2

Elements Of Electromagnetics
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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PART OF MECHANICAL VIBRATIONS

 

Derive the differential equation of motion of the inverted pendulum shown
in Fig. P3.8. Let m = 0.5 kg, l = 0.5 m, a = 0.2 m, and k = 3000 N/m. Determine the damping coefficient c if: (a) the system is underdamped with
ξ = 0.09, (b) the system is critically damped; and (c) the system is over-damped with ξ = 1.2. In these three cases determine the angular displacement
and velocity after 0.4 s if the system has zero initial velocity and initial
displacement of 4◦ counterclockwise

m a Fig. P3.8
Transcribed Image Text:m a Fig. P3.8
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