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3.19. Derive the differential equation of motion of the inverted pendulum shown in Fig. P3.8. Let m =0.5 kg, I=0.5 m, a=0.2 m, and k = 3000 N/m. Deter- mine the damping coefficient c if: (a) the system is underdamped with $ =0.09, (b) the system is critically damped; and (c) the system is over-

3.19. Derive the differential equation of motion of the inverted pendulum shown in Fig. P3.8. Let m =0.5 kg, I=0.5 m, a=0.2 m, and k = 3000 N/m. Deter- mine the damping coefficient c if: (a) the system is underdamped with $ =0.09, (b) the system is critically damped; and (c) the system is over-

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
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3.19. Derive the differential equation of motion of the inverted pendulum shown in Fig. P3.8. Let m=0.5 kg, 1=0.5 m, a=0.2m, and k = 3000 N/m. Deter- mine the damping coefficient c if: (a) the system is underdamped with $ =0.09, (b) the system is critically damped; and (c) the system is over- Problems 125 damped with & = 1.2. In these three cases determine the angular displacement and velocity after 0.4s if the system has zero initial velocity and initial displacement of 4° counterclockwise. m a Fig. P3.8
Transcribed Image Text:3.19. Derive the differential equation of motion of the inverted pendulum shown in Fig. P3.8. Let m=0.5 kg, 1=0.5 m, a=0.2m, and k = 3000 N/m. Deter- mine the damping coefficient c if: (a) the system is underdamped with $ =0.09, (b) the system is critically damped; and (c) the system is over- Problems 125 damped with & = 1.2. In these three cases determine the angular displacement and velocity after 0.4s if the system has zero initial velocity and initial displacement of 4° counterclockwise. m a Fig. P3.8
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