a) A two-degree-of-freedom coupled pendulum model is shown in Figure Q1a.The parameters of the model are: k=100 N/m; m=10 kg and L=1 m. Theequations of motion of the system are given below.J₁ä + (mgL + kĽ² ) 8₁ - kľ² 0₁₂ = 0J₁₂+(mgL+kĽ²)₂-kĽ² 0₁ = 0i) Calculate the natural frequencies.ii)Draw the mode shapes.mFigure Q1a.b) In the above system discuss the implications of the following changes incoupling stiffness.i) k is reduced considerably to 0.1 N/m.ii) k is increased considerably to 1x105 N/m.c) Draw a schematic of modal test arrangement of a beam using instrumentedimpact hammer.d) Why is it necessary to measure force in a modal test?

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a) A two-degree-of-freedom coupled pendulum model is shown in Figure Q1a. The parameters of the model are: k=100 N/m; m=10 kg and L=1 m. The equations of motion of the system are given below. J₁₁ +(mgL + kĽ²)Q₁ – kĽ²Ð₁₂ = 0 J₁₁₂+(mgL+kĽ²)0₂-kĽ² 0₁₂ = 0 i) Calculate the natural frequencies. ii) Draw the mode shapes. Figure Q1a. b) In the above system discuss the implications of the following changes in coupling stiffness. i) k is reduced considerably to 0.1 N/m. ii) k is increased considerably to 1x105 N/m. c) Draw a schematic of modal test arrangement of a beam using instrumented

a) A two-degree-of-freedom coupled pendulum model is shown in Figure Q1a. The parameters of the model are: k=100 N/m; m=10 kg and L=1 m. The equations of motion of the system are given below. J₁₁ +(mgL + kĽ²)Q₁ – kĽ²Ð₁₂ = 0 J₁₁₂+(mgL+kĽ²)0₂-kĽ² 0₁₂ = 0 i) Calculate the natural frequencies. ii) Draw the mode shapes. Figure Q1a. b) In the above system discuss the implications of the following changes in coupling stiffness. i) k is reduced considerably to 0.1 N/m. ii) k is increased considerably to 1x105 N/m. c) Draw a schematic of modal test arrangement of a beam using instrumented

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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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

a) A two-degree-of-freedom coupled pendulum model is shown in Figure Q1a.
The parameters of the model are: k=100 N/m; m=10 kg and L=1 m. The
equations of motion of the system are given below.
J₁ä + (mgL + kĽ² ) 8₁ - kľ² 0₁₂ = 0
J₁₂+(mgL+kĽ²)₂-kĽ² 0₁ = 0
i) Calculate the natural frequencies.
ii)
Draw the mode shapes.
m
Figure Q1a.
b) In the above system discuss the implications of the following changes in
coupling stiffness.
i) k is reduced considerably to 0.1 N/m.
ii) k is increased considerably to 1x105 N/m.
c) Draw a schematic of modal test arrangement of a beam using instrumented
impact hammer.
d) Why is it necessary to measure force in a modal test?

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