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A support beam 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 nodelled by the following equations,x, = 3.75 sin (100zt + mm X2 = 4.42 sin (100nt mm a. State the amplitude, phase, frequency and periodic time of each of these waves. b. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? c. At what time does each vibration first reach a displacement of -2mm? d. Use the compound angle formulae to expand x, and x2 into the form A sin 100nt ±

A support beam 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 nodelled by the following equations,x, = 3.75 sin (100zt + mm X2 = 4.42 sin (100nt mm a. State the amplitude, phase, frequency and periodic time of each of these waves. b. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? c. At what time does each vibration first reach a displacement of -2mm? d. Use the compound angle formulae to expand x, and x2 into the form A sin 100nt ±

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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Task 4 A support beam 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 (100rt + mm x2 = 4.42 sin (100nt mm a. State the amplitude, phase, frequency and periodic time of each of these waves. b. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? c. At what time does each vibration first reach a displacement of – 2mm? d. Use the compound angle formulae to expand x, and x2 into the form A sin 100rt ± B cos 100nt, where A and B are numbers to be found. e. Using your answers from part d, express ( x, + x2), ( 2x, - 4x2), and ( x1 + x2)( 2x - 4x2) in a similar forms. Convert this expression into the equivalent forms of R sin(100nbt + a). f. Express the 10th term of ( x, + x,)20 in terms of sinusoidal functions (sin, cos). g. Using appropriate spreadsheet software, copy and complete the following table of values: 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 X2 h. Plot the graphs of x, and x2 on the same axes using any suitable computer package. Extend your table to include x, + x2, X1- X2, and plot these graphs on the same axes as the previous two. State the amplitude and frequency of the new wave. Repeat for e and f. i. Using your answers from parts g and h, what conclusions can be drawn about x, + x2 and the two methods that were used to obtain this information? Task 5
Transcribed Image Text:Task 4 A support beam 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 (100rt + mm x2 = 4.42 sin (100nt mm a. State the amplitude, phase, frequency and periodic time of each of these waves. b. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? c. At what time does each vibration first reach a displacement of – 2mm? d. Use the compound angle formulae to expand x, and x2 into the form A sin 100rt ± B cos 100nt, where A and B are numbers to be found. e. Using your answers from part d, express ( x, + x2), ( 2x, - 4x2), and ( x1 + x2)( 2x - 4x2) in a similar forms. Convert this expression into the equivalent forms of R sin(100nbt + a). f. Express the 10th term of ( x, + x,)20 in terms of sinusoidal functions (sin, cos). g. Using appropriate spreadsheet software, copy and complete the following table of values: 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 X2 h. Plot the graphs of x, and x2 on the same axes using any suitable computer package. Extend your table to include x, + x2, X1- X2, and plot these graphs on the same axes as the previous two. State the amplitude and frequency of the new wave. Repeat for e and f. i. Using your answers from parts g and h, what conclusions can be drawn about x, + x2 and the two methods that were used to obtain this information? Task 5
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