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A support beam used in one of the designs for the theme park, 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 (100πt + x₂ = 4.42 sin (100πt - 2π 9) 2πT 5

A support beam used in one of the designs for the theme park, 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 (100πt + x₂ = 4.42 sin (100πt - 2π 9) 2πT 5

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Trigonometry
Section: Chapter Questions
Problem 2T
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For the attached scenario, substitute the t values and complete the table for the attached question 4?

A support beam used in one of the designs for the theme park, 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 + x₂ = 4.42 sin (100πt - 2πT 9) 2π 5
Transcribed Image Text:A support beam used in one of the designs for the theme park, 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 + x₂ = 4.42 sin (100πt - 2πT 9) 2π 5
4. Using appropriate spread sheet software, copy and complete the following table of values: t 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 X1 X₂
Transcribed Image Text:4. Using appropriate spread sheet software, copy and complete the following table of values: t 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 X1 X₂
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Follow-up Question

Answer v provided in attached image.

Can you now answer question viii?(attached image)

v. Using your answers from part iv, express x₁ + x₂ in a similar form. Convert this expression into the equivalent form R sin (100πt + a) 2.8726 sin (100nt) + 2.41045 cos (100nt) X₁ = X₂ = 1.3658 sin (100nt) - 4.2036 cos (100nt) x₁ + x₂= R sin (100πt + a) R = {(4.2384)² + (-1.79315)²31/2 R = 4.60211 -1.79315 4.2389 x₁ + x₂ = 4.60211 Sin(100nt - 22.932°) a tan = -22.932°
Transcribed Image Text:v. Using your answers from part iv, express x₁ + x₂ in a similar form. Convert this expression into the equivalent form R sin (100πt + a) 2.8726 sin (100nt) + 2.41045 cos (100nt) X₁ = X₂ = 1.3658 sin (100nt) - 4.2036 cos (100nt) x₁ + x₂= R sin (100πt + a) R = {(4.2384)² + (-1.79315)²31/2 R = 4.60211 -1.79315 4.2389 x₁ + x₂ = 4.60211 Sin(100nt - 22.932°) a tan = -22.932°
viii. Using your answers from parts v and vii, what conclusions can be drawn about x₁ + x2 and the two methods that were used to obtain this information?
Transcribed Image Text:viii. Using your answers from parts v and vii, what conclusions can be drawn about x₁ + x2 and the two methods that were used to obtain this information?
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Follow-up Question

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vii. Plot the graphs of x₁ and x₂ on the same axes using any suitable computer package. Extend your table to include x₁ + x₂ and plot this graph on the same axes as the previous two. State the amplitude and frequency of the new wave. viii. Using your answers from parts v and vii, what conclusions can be drawn about x₁ + x₂ and the two methods that were used to obtain this information?
Transcribed Image Text:vii. Plot the graphs of x₁ and x₂ on the same axes using any suitable computer package. Extend your table to include x₁ + x₂ and plot this graph on the same axes as the previous two. State the amplitude and frequency of the new wave. viii. Using your answers from parts v and vii, what conclusions can be drawn about x₁ + x₂ and the two methods that were used to obtain this information?
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