TASK 3Scenario 1A support beam, within an industrial building, is subjected to vibrations along its length; emanating from twomachines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelledby 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 produceits 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 theequivalent form Rsin(100nt + x).Model x1+x2 waves graphically and analyse the variation between graphical and analyticalmethods

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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.

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

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

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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