Q₁: The system shown has two masses. Beam of mass (J.*m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? L/2 A Jo=m L² k L/2 Joz-m R² R H B с 120

Q₁: The system shown has two masses. Beam of mass (J.*m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? L/2 A Jo=m L² k L/2 Joz-m R² R H B с 120

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 undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

Q1: The system shown has two masses. Beam of mass (Jo#m L²
kg.m²) rotates about fixed point (O) and its free end is connected to
disk rotates about fixed point (O₂). Consider all connecting links are
massless and rigid. Find
1- The displacements of points A, B, and C in addition to the
rotations of masses, all in terms of 0.
2- Find the equation of motion (EOM) in terms of 0.
3- What is the natural frequency of the system?
L/2
A
Jo=m L²
k
L/2
Joz-m R²
full
0₂
R
U
B
C

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Step 1: Given:

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Step 2: Finding the displacement of point A, B and C :

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Step 3: The equation of motion is :

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Step 4: The natural frequency of the system :

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