Q1: A machine is modelled by the system shown. The masses of the main elements and m2, and the spring stiffnesses are as shown in Fig 2.4. Each roller has a are m1, mass m, diameter d, and mass moment of inertia J about its axis, and rolls without slipping. Considering motion in the longitudinal direction only, use Lagrange's equation to obtain the equations of motion for small free oscillations of the system. md² /8, deduce the natural frequencies Given that m1 3 4m, т, 3 %3 2m, and J of the system and the corresponding mode shapes. m, m2 k 4k ovo Fig. 2.4

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
icon
Related questions
Question
Q1: A machine is modelled by the system shown. The masses of the main elements
are m1, and m2, and the spring stiffnesses are as shown in Fig 2.4. Each roller has a
mass m, diameter d, and mass moment of inertia J about its axis, and rolls without
slipping. Considering motion in the longitudinal direction only, use Lagrange's
equation to obtain the equations of motion for small free oscillations of the system.
Given that m, = 4m, m2 = 2m, and J = md² /8, deduce the natural frequencies
%3D
%3D
%3D
of the system and the corresponding mode shapes.
m2
4k
evo Fig. 2.4
ww
Transcribed Image Text:Q1: A machine is modelled by the system shown. The masses of the main elements are m1, and m2, and the spring stiffnesses are as shown in Fig 2.4. Each roller has a mass m, diameter d, and mass moment of inertia J about its axis, and rolls without slipping. Considering motion in the longitudinal direction only, use Lagrange's equation to obtain the equations of motion for small free oscillations of the system. Given that m, = 4m, m2 = 2m, and J = md² /8, deduce the natural frequencies %3D %3D %3D of the system and the corresponding mode shapes. m2 4k evo Fig. 2.4 ww
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Free Undamped Vibrations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY