We will use MATLAB to find the decay constant C and the period T. We can then use these to calculate the damping ratio 3 and the natural frequency wn, using: wa = wn√√1-3² = 2πT T 3 = and C = 3Wn Using the information above, derive the expression shown below for the damping ratio 3. 1 2 √₁ + (²77) ² 2π

We will use MATLAB to find the decay constant C and the period T. We can then use these to calculate the damping ratio 3 and the natural frequency wn, using: wa = wn√√1-3² = 2πT T 3 = and C = 3Wn Using the information above, derive the expression shown below for the damping ratio 3. 1 2 √₁ + (²77) ² 2π

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 Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

The plot below shows the acceleration of a mass placed at the end of a beam as it oscillates:
20
Which we model as:
Acceleration (m/s²)
15
10
5
0
-5
-10
-15
-20
0.5
1
Wd
1
1.5
1
2
= wn√1
y(t) = Ae-3wnt sin(wat)
y(t) = Ae-Ct sin
1
2.5
Time (s)
=
2π
T
2π
T
1+
3
2π
We will use MATLAB to find the decay constant C and the period T.
We can then use these to calculate the damping ratio and the natural frequency @n, using:
3.5
T
4
2
and C = {wn
O
data
zeros
peaks
decay fit
4.5
Using the information above, derive the expression shown below for the damping ratio 3.
1
3 =
5

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