Derive the Lagrange's Equations of motion for the system shown in Fig. 1 using the displacement x as the generalized coordinate of the mass m. Assume that the pulley and the mass m are rigidly coupled: Find the steady-state response of the system for the following data: = 1000N / m,k = 500N / m, c = 500NS / m, m=10kg,r = 5cm,J, = 1kgm² , F, = 50N, @= 20rad / s. %3D %3D %3D %D %3! %3D Pulley, mass moment of inertia J C000 2r Fosin ast Fig. 1

Derive the Lagrange's Equations of motion for the system shown in Fig. 1 using the displacement x as the generalized coordinate of the mass m. Assume that the pulley and the mass m are rigidly coupled: Find the steady-state response of the system for the following data: = 1000N / m,k = 500N / m, c = 500NS / m, m=10kg,r = 5cm,J, = 1kgm² , F, = 50N, @= 20rad / s. %3D %3D %3D %D %3! %3D Pulley, mass moment of inertia J C000 2r Fosin ast Fig. 1

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

Derive the Lagrange's Equations of motion for the system shown in Fig. 1 using the
displacement x as the generalized coordinate of the mass m. Assume that the pulley and the
mass m are rigidly coupled:
Find the steady-state response of the system for the following data:
k = 1000N / m,k, = 500N / m, c = 500NS / m, m =10kg,r = 5cm,J, = 1kgm² , F, = 50N, @= 20rad / s.
%3D
%3D
%3D
%3D
%3D
Pulley, mass moment of inertia J
2r
Fosin ast
Fig. 1

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