Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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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?

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