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 in conditions x₁ (0) = 1cm, and x₂ (0) = x₁(0) = x₂(0) = 0. h 2h 2k 2k 2m 0.5K k m Tu2 0.5K Tul k

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 in conditions x₁ (0) = 1cm, and x₂ (0) = x₁(0) = x₂(0) = 0. h 2h 2k 2k 2m 0.5K k m Tu2 0.5K Tul k

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

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.
h
2h
2k
2k
mmm
2m
0.5K
k
Figure 5
m
Tu2
0.5K
Hul
k

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Step 1: Given data

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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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