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,x, = 3.75 sin (100t +) mm x2 = 4.42 sin (100mt - mm a. State the amplitude, phase, frequency and periodic time of each of these waves ives. b. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement?
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,x, = 3.75 sin (100t +) mm x2 = 4.42 sin (100mt - mm a. State the amplitude, phase, frequency and periodic time of each of these waves ives. b. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement?
Related questions
Question
Answer Task (4), part (a) & (b).
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.x, = 3.75 sin (100nt +) mm
x2 = 4.42 sin (100t -) 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 x, into the form A sin 100nt +
B cos 100nt, where A and B are numbers to be found.
e. Using your answers from part d, express ( x1 + x2), ( 2x1- 4x2), and (x1 + x2)( 2x1 -
4x2) in a similar forms. Convert this expression into the equivalent forms of
R sin(100rbt + a).
f. Express the 10th term of ( x1 + x2)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
h. Plot the graphs of x, and x, on the same axes using any suitable computer package.
Extend your table to include x1 + 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 x1 + x2
and the two methods that were used to obtain this information?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
