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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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
Transcribed Image Text: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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