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 + 2m/9) x2 = 4.42 sin (100nt – 21/5) i State the amplitude, phase, frequency and periodic time of each of these waves. ii. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? Atwhattimedoes eachvibrationfirstreachadisplacementof –2mm? iv. Use the compound angle formulae to expand xland x2 into the form A sin 100mt + B cos 100nt, where A and B are numbers to be found. v. Using your answers from part iv, express x1 + x2 in a similar form. Convert this expression into the equivalent form Rsin(100nt +c).
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 + 2m/9) x2 = 4.42 sin (100nt – 21/5) i State the amplitude, phase, frequency and periodic time of each of these waves. ii. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? Atwhattimedoes eachvibrationfirstreachadisplacementof –2mm? iv. Use the compound angle formulae to expand xland x2 into the form A sin 100mt + B cos 100nt, where A and B are numbers to be found. v. Using your answers from part iv, express x1 + x2 in a similar form. Convert this expression into the equivalent form Rsin(100nt +c).
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People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
Question
Transcribed Image Text: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 + 2m/9)
x2 = 4.42 sin (100rt – 2m/5 )
i State the amplitude, phase, frequency and periodic time of each of these waves.
ii. When both machines are switched on, how many seconds does it take for each machine to produce
its maximum displacement?
. Atwhattime does eachvibrationfirstreachadisplacementof–2mm?
iv. Use the compound angle formulae to expand xland x2 into the form A sin 100mt ± B cos 100mt, where
A and B are numbers to be found.
v. Using your answers from part iv, express x1 + x2 in a similar form. Convert this expression into the
equivalent form Rsin(100nt + o3).
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Transcribed Image Text:L03 Use analytical and computational methods for solving problems by relating sinusoidal wave and
vector functions to their respective construction applications
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.
i.
ii.
iii.
iv.
V.
vi.
x1 = 3.75 sin (100nt + 2π/9)
x2 = 4.42 sin (100πt - 2π/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 eachvibration first reach a displacement of -2mm?
Use the compound angle formulae to expand x1and x2 into the form A sin 100πt ± 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 + ac).
Model x1+x2 waves graphically and analyse the variation between graphical and analytical
methods
Solution
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