Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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.
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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.
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