A support beam, within an industrial building, 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.

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
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TASK 3
Scenario 1
A support beam, within an industrial building, 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 + 27/9)
i.
ii.
iii.
iv.
V.
vi.
x2 = 4.42 sin (100πt-2n/5)
State the amplitude, phase, frequency and periodic time of each of these waves.
When both machines are switched on, how many seconds does it take for each machine to produce
its maximum displacement?
At what time does each vibration first reach a displacement of -2mm?
Use the compound angle formulae to expand x1and x2 into the form A sin 100nt ± B cos 100nt,
where A and B are numbers to be found.
Using your answers from part iv, express x1 + x2 in a similar form. Convert this expression into the
equivalent form Rsin(100nt + x).
Model x1+x2 waves graphically and analyse the variation between graphical and analytical
methods
Transcribed Image Text:TASK 3 Scenario 1 A support beam, within an industrial building, 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 + 27/9) i. ii. iii. iv. V. vi. x2 = 4.42 sin (100πt-2n/5) State the amplitude, phase, frequency and periodic time of each of these waves. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? At what time does each vibration first reach a displacement of -2mm? Use the compound angle formulae to expand x1and x2 into the form A sin 100nt ± B cos 100nt, where A and B are numbers to be found. Using your answers from part iv, express x1 + x2 in a similar form. Convert this expression into the equivalent form Rsin(100nt + x). Model x1+x2 waves graphically and analyse the variation between graphical and analytical methods
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