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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. 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).

Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter18: Superposition And Standing Waves
Section: Chapter Questions
Problem 18.4OQ
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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. 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).
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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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
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
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