PROBLEMS: a)Find the natural frequencies and mode shapes of the system shown in Figure 5. b) Find the free-vibration response of the two-degree-of-freedom system shown in Figure 5 with the initial conditions x₁ (0) = 1cm, and x₂ (0) = x₁(0) = x₂(0) = 0.

PROBLEMS: a)Find the natural frequencies and mode shapes of the system shown in Figure 5. b) Find the free-vibration response of the two-degree-of-freedom system shown in Figure 5 with the initial conditions x₁ (0) = 1cm, and x₂ (0) = x₁(0) = x₂(0) = 0.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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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

PROBLEM5:
a)Find the natural frequencies and mode shapes of the system shown in Figure 5.
b) Find the free-vibration response of the two-degree-of-freedom system shown in Figure 5 with the initial
conditions x₁ (0) = 1cm, and x₂ (0) = x₁(0) = x₂(0) = 0.
Good luck
h
2h
2k
2k
mmm
2m
0.5K
k
mm
Figure 5
m
Tu2
0.5K
Tul
k
mm

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Step 2: Deriving the equations of motion

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Step 3: Natural frequencies and natural modes of the system

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Step 4: Free vibration response of the system

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