How much must the excitation frequency be changed in order for the amplitude of the device to decrease to the value x=1 mm?
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=ωn.
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?
Transcribed Image Text: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?
Expert Solution
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Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Calculate the initial frequency ratio and natural frequency.
VIEWStep 2: Write the equation for amplitude of steady state response.
VIEWStep 3: Take the ratio of final steady state amplitude to initial steady state.
VIEWStep 4: Substitute the given values.
VIEWStep 5: Solve the final excitation frequency.
VIEWStep 6: Determine the change in excitation frequency in order for the amplitude of the device to decrease.
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