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) = cm, v (0) = m Sec 5k 0888

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) = cm, v (0) = m Sec 5k 0888

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

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

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)
m
(2)
{2} cm.
=
cm, v (0)
Sec
00000 m
k
00000
k
x₂ (1)
5k
0000
Figure 3
00000
k
x₂ (1)
m
00000
k
X3 (1)

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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