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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

100%

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

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 Questions

Read through expert solutions to related follow-up questions below.

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°

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?

Solution

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Follow-up Question

Please see the attached follow up questions.

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?

Solution

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