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. Thedisplacement 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 eachmachine to produce its maximum displacement?tX1X2ii) 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 formAsin (100nt)+Bcos (100nt), where A and B are constant numbers to be found.1v) Using your answers from part (iv), express x₁ + x, in a similar form, and convert thisexpression into the equivalent form: R sin(100nt + a).vi) Using appropriate spreadsheet software, copy and complete the following table ofvalues:0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020(xeel)1vii) 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 theprevious two. State the amplitude and frequency of the new wave.1: x₁₂ + x ₂ i1viii) Using your answers from parts v and vii, what conclusions can be drawn about x + xin addition, analyse the variation between the graphical and analytical methods youhave used.

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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: = 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.

Electric Motor Control

10th Edition

ISBN:9781133702818

Author:Herman

Publisher:Herman

Chapter3: Magnetic Starters

Section: Chapter Questions

Problem 30SQ

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