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( 100nt + 2n mm 2n) 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?

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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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
2n
modelled by the following equations,x1 = 3.75 sin ( 100nt +) mm
9
x2 = 4.42 sin (100nt – 4)
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 x1 and x2 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 ( x + x2), ( 2x1 – 4x2), and ( x1 + X2)( 2x1 -
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:
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: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 2n modelled by the following equations,x1 = 3.75 sin ( 100nt +) mm 9 x2 = 4.42 sin (100nt – 4) 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 x1 and x2 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 ( x + x2), ( 2x1 – 4x2), and ( x1 + X2)( 2x1 - 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: 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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