Consider a system of a uniform disc of mass Md and radius r attached on a vertical uniformrectangular rod of mass M which is constrained to oscillate left and right at a pivot pointO by a harmonic excition force F = F, sin 50t applied at the top extremity of the rod asshown in the Figure Q1.For M=10kg M, = 5kg, F, =75N,k=8kN/m, c=360NS/m, r=0.12m and L=1.2m. 1.1Draw the free body diagram with all the forces applied to the system;1.2Find the equation of motion for small displacement of the bar;1.3Determine the frequency of damped vibrations of the system in Hz; and1.4Determine the maximum amplitude of B due to the varying excitation force.F = F, sin 50fDL/6CL/3L/4klellBL/4AFigure Q1

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Consider a system of a uniform disc of mass Md and radius r attached on a vertical uniform rectangular rod of mass M which is constrained to oscillate left and right at a pivot point O by a harmonic excition force F = F, sin50t applied at the top extremity of the rod as shown in the Figure Q1. For M=10kg M, = 5kg, F, = 75N,k=8kN/m, c=360NS/m, r=0.12m and L=1.2m. %3D

Consider a system of a uniform disc of mass Md and radius r attached on a vertical uniform rectangular rod of mass M which is constrained to oscillate left and right at a pivot point O by a harmonic excition force F = F, sin50t applied at the top extremity of the rod as shown in the Figure Q1. For M=10kg M, = 5kg, F, = 75N,k=8kN/m, c=360NS/m, r=0.12m and L=1.2m. %3D

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

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Consider a system of a uniform disc of mass Md and radius r attached on a vertical uniform
rectangular rod of mass M which is constrained to oscillate left and right at a pivot point
O by a harmonic excition force F = F, sin 50t applied at the top extremity of the rod as
shown in the Figure Q1.
For M=10kg M, = 5kg, F, =75N,k=8kN/m, c=360NS/m, r=0.12m and L=1.2m.

1.1
Draw the free body diagram with all the forces applied to the system;
1.2
Find the equation of motion for small displacement of the bar;
1.3
Determine the frequency of damped vibrations of the system in Hz; and
1.4
Determine the maximum amplitude of B due to the varying excitation force.
F = F, sin 50f
D
L/6
C
L/3
L/4
k
lell
B
L/4
A
Figure Q1

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