Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
A support beam within an industrial building is subjected to vibrations along its length, which originate from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations: = 3.75sin (100nt) x₁ = = 5.17sin (150nt) x₂ = i) When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? ii) At what time does each vibration first reach a displacement of 2 mm? iii) Derive a formula that shows when x, = x₂ = 0.

A support beam within an industrial building is subjected to vibrations along its length, which originate from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations: = 3.75sin (100nt) x₁ = = 5.17sin (150nt) x₂ = i) When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? ii) At what time does each vibration first reach a displacement of 2 mm? iii) Derive a formula that shows when x, = x₂ = 0.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question
A support beam within an industrial building is subjected to vibrations along its length, which originate from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations: x₁ = 1 = 3.75sin (100nt) X2 = 5.17sin (150nt) i) When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? t X1 X2 ii) At what time does each vibration first reach a displacement of 2 mm? iii) Derive a formula that shows when xy = x₂ = 0. iv) Use the compound angle formulae to expand x and x into the form Asin (100nt)+Bcos (100nt), where A and B are constant numbers to be found. 1 v) Using your answers from part (iv), express x₁ + x, in a similar form, and convert this expression into the equivalent form: R sin(100nt + a). vi) Using appropriate spreadsheet software, copy and complete the following table of values: 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 (xeel) 1 vii) Plot the graphs of x and x on the same axes using any suitable computer package. Extend your table to include x + x and plot this graph on the same axes as the previous two. State the amplitude and frequency of the new wave. 1 : x₁₂ + x ₂ i 1 viii) Using your answers from parts v and vii, what conclusions can be drawn about x + x in addition, analyse the variation between the graphical and analytical methods you have used.
Transcribed Image Text:A support beam within an industrial building is subjected to vibrations along its length, which originate from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations: x₁ = 1 = 3.75sin (100nt) X2 = 5.17sin (150nt) i) When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? t X1 X2 ii) At what time does each vibration first reach a displacement of 2 mm? iii) Derive a formula that shows when xy = x₂ = 0. iv) Use the compound angle formulae to expand x and x into the form Asin (100nt)+Bcos (100nt), where A and B are constant numbers to be found. 1 v) Using your answers from part (iv), express x₁ + x, in a similar form, and convert this expression into the equivalent form: R sin(100nt + a). vi) Using appropriate spreadsheet software, copy and complete the following table of values: 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 (xeel) 1 vii) Plot the graphs of x and x on the same axes using any suitable computer package. Extend your table to include x + x and plot this graph on the same axes as the previous two. State the amplitude and frequency of the new wave. 1 : x₁₂ + x ₂ i 1 viii) Using your answers from parts v and vii, what conclusions can be drawn about x + x in addition, analyse the variation between the graphical and analytical methods you have used.
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Speed control of motor
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS