A support beam used in one of the designs for the theme park, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations: x_1=3.75 sin⁡(100πt+2π/9)x_2=4.42 sin⁡(100πt-2π/5)You are required to determine the followings for the vibration of this beam:i. State the amplitude, phase angle, frequency and periodic time of each of these waves.ii. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement?iii. At what time does each vibration first reach a displacement of −2???iv. Use the compound angle formulae to expand x_1 and x_2 into the form ? sin 100?? ± ? cos 100??, where ? and ? are numbers to be found.v. Using your answers from part iv, express x_1+x_2 in a similar form. Convert this expression into the equivalent form ? sin (100?? + α) AutoSave OffFilePasteHHHomeX CutInsert DrawCopyFormat PainterArialDesignBIU ab2901 wordsUnit 2 Engineering Maths Module Brief - 2022-2023 (1).docx . Saved to this PCLayout References Mailings Review1:=-1¹5-A A Aa AView Help←= = 2 ↓ वाDE = = 闫~x ADA12X₂ClipboardFontParagraphthat the rate of change of with respect to follows an exponential model of the formdtaekt during the first quarter of the ride and debe-mt during the second quarter with a, b,Suggest possible values for the constants mentioned and use them to evaluate the anglethrough which a rider goes between the time intervals of t = 100 sec and of t = 300 secdtm and k all being constants. The same patterns are followed during the second half of theride. The wheel diameter and ride duration still unchanged.Part 2:A support beam used in one of the designs for the theme park, is subjected to vibrations alongits length; emanating from two machines situated at opposite ends of the beam. Thedisplacement caused by the vibrations can be modelled by the following equations:x₁ = 3.75 sin (100nt +x₂ = 4.42 sin (100nt -2π952πYou are required to determine the followings for the vibration of this beam:i. State the amplitude, phase angle, frequency and periodic time of each of these waves.ii. When both machines are switched on, how many seconds does it take for each machine toproduce its maximum displacement?iii. At what time does each vibration first reach a displacement of -2mm?iv. Use the compound angle formulae to expand x₁ and x₂ into the formA sin 100nt + B cos 100nt, where A and B are numbers to be found.v. Using your answers from part iv, express x₁ + x₂ in a similar form. Convert this expression intothe equivalent form R sin (100nt + a)vi. Using appropriate spread sheet software, copy and complete the following table of values:0.000 0.002 0.001 0.006 0.008 0.010 0012 0011 0016 0.018 0020叹 English (United Kingdom)Accessibility: InvestigateType here to searchE0SearchTable DesignAaBbc AaBb( AaBbCc AaBbC AaBbCc AaBbCcI AaBbCcI AaBbCcI AaBbCcD AaB AaBbcct AaBbCcD AaBbCcDHeading 1Heading 2 No Spac...Assignm... Qualific... Body TextNormalTable Pa... Heading 3. TitleSubtitleSubtle Em...EmphasisWLayoutPawel Wardzynski PWStylesFocus 802°C CloudyO FindECommentsReplaceSelectEditingActivate WindowsGo to Settings to activate Windows.eDictateVoice4) POLShare ✔EditorEditor+ 100%22:4322/01/2023 1

Given: x1=3.75 sin100πt+2π9x2=4.42 sin100πt-2π5 To find: The amplitude, phase angle, frequency and…

Answered: A support beam used in one of the…

Elements Of Electromagnetics

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Author:Sadiku, Matthew N. O.

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A support beam used in one of the designs for the theme park, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations:

x_1=3.75 sin⁡(100πt+2π/9)

x_2=4.42 sin⁡(100πt-2π/5)

You are required to determine the followings for the vibration of this beam:

i. State the amplitude, phase angle, frequency and periodic time of each of these waves.

ii. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement?

iii. At what time does each vibration first reach a displacement of −2???

iv. Use the compound angle formulae to expand x_1 and x_2 into the form
? sin 100?? ± ? cos 100??, where ? and ? are numbers to be found.

v. Using your answers from part iv, express x_1+x_2 in a similar form. Convert this expression into the equivalent form ? sin (100?? + α)

AutoSave Off
File
Paste
HH
Home
X Cut
Insert Draw
Copy
Format Painter
Arial
Design
BIU ab
2901 words
Unit 2 Engineering Maths Module Brief - 2022-2023 (1).docx . Saved to this PC
Layout References Mailings Review
1:=-1¹5-
A A Aa A
View Help
←= = 2 ↓ वा
DE = = 闫~
x ADA
12
X₂
Clipboard
Font
Paragraph
that the rate of change of with respect to follows an exponential model of the form
dt
aekt during the first quarter of the ride and debe-mt during the second quarter with a, b,
Suggest possible values for the constants mentioned and use them to evaluate the angle
through which a rider goes between the time intervals of t = 100 sec and of t = 300 sec
dt
m and k all being constants. The same patterns are followed during the second half of the
ride. The wheel diameter and ride duration still unchanged.
Part 2:
A support beam used in one of the designs for the theme park, is subjected to vibrations along
its length; emanating from two machines situated at opposite ends of the beam. The
displacement caused by the vibrations can be modelled by the following equations:
x₁ = 3.75 sin (100nt +
x₂ = 4.42 sin (100nt -
2π
9
5
2π
You are required to determine the followings for the vibration of this beam:
i. State the amplitude, phase angle, frequency and periodic time of each of these waves.
ii. When both machines are switched on, how many seconds does it take for each machine to
produce its maximum displacement?
iii. At what time does each vibration first reach a displacement of -2mm?
iv. Use the compound angle formulae to expand x₁ and x₂ into the form
A sin 100nt + B cos 100nt, where A and B are numbers to be found.
v. Using your answers from part iv, express x₁ + x₂ in a similar form. Convert this expression into
the equivalent form R sin (100nt + a)
vi. Using appropriate spread sheet software, copy and complete the following table of values:
0.000 0.002 0.001 0.006 0.008 0.010 0012 0011 0016 0.018 0020
叹 English (United Kingdom)
Accessibility: Investigate
Type here to search
E
0
Search
Table Design
AaBbc AaBb( AaBbCc AaBbC AaBbCc AaBbCcI AaBbCcI AaBbCcI AaBbCcD AaB AaBbcct AaBbCcD AaBbCcD
Heading 1
Heading 2 No Spac...
Assignm... Qualific... Body Text
Normal
Table Pa... Heading 3. Title
Subtitle
Subtle Em...
Emphasis
W
Layout
Pawel Wardzynski PW
Styles
Focus 80
2°C Cloudy
O Find
E
Comments
Replace
Select
Editing
Activate Windows
Go to Settings to activate Windows.
e
Dictate
Voice
4) POL
Share ✔
Editor
Editor
+ 100%
22:43
22/01/2023 1

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for Part V) should the answer not be -0.4 to the final part of the question since the number put into the equasion is -1.79

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