PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v (0) = {1} cm. v (0) = ܠܠܠܠܠܠܠܝ 00000 k m Sec m 00000 k x1 (1) 5k 0000 m Figure 3 00000 k x₂ (1) 6000 kN/m. m 00000 k x3 (1) ܠܠܠܠܠܠܝ

PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v (0) = {1} cm. v (0) = ܠܠܠܠܠܠܠܝ 00000 k m Sec m 00000 k x1 (1) 5k 0000 m Figure 3 00000 k x₂ (1) 6000 kN/m. m 00000 k x3 (1) ܠܠܠܠܠܠܝ

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

PROBLEM3:
Consider the system shown in Figure 3, where m = 70 ton and k = 6000 kN/m.
d) Derive the equations of motion.
e) Find the natural frequencies and mode shapes of the system.
f) Find the free-vibration response of the system for the initial conditions:
v(0)=
{1} cm
cm, v (0) =
m
Sec
00000 m
k
00000
k
x₁ (1)
Jour
5k
0000
m
Figure 3
00000 m 00000
k
k
x₂(1)
- X3 (1)
ܠܠܠܠܠܠܠܝ

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