Answered: How much must the excitation frequency…

How much must the excitation frequency be changed in order for the amplitude of the device to decrease to the value x=1 mm?

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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Question

The amplitude of the steady-state response of a single-degree-of-freedom device is x=5 mm, when the excitation frequency is Ω=ω_n.

System mass m=200 kg. Fastening stiffness k=30 kNm and damping ratio ς=0.1. The system is loaded by the force F(t)=e^(i*Ω*t).

How much must the excitation frequency be changed in order for the amplitude of the device to decrease to the value x=1 mm?

X
m
F(t)
*{A•
Yksivapausasteisen laitteen vakiotilavasteen amplitudi
X = 5 mm, kun herätteen taajuus Q = wn.
Systeemin m = 200 kg. Kiinnityksen jäykkyys k = 30 kNm
ja vaimennussuhde = 0.1. Systeemiä kuormittaa voima
F(t) = eit
Kuinka paljon herätetaajuutta pitää muuttaa, jotta laitteen
amplitudi pienenisi arvoon X = 1 mm?

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Step 1: Calculate the initial frequency ratio and natural frequency.

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Step 2: Write the equation for amplitude of steady state response.

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Step 3: Take the ratio of final steady state amplitude to initial steady state.

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Step 4: Substitute the given values.

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Step 5: Solve the final excitation frequency.

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Step 6: Determine the change in excitation frequency in order for the amplitude of the device to decrease.

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