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 ( 100t + 2n mm x2 = 4.42 sin (100tt 2n 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?

University Physics Volume 1
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Chapter16: Waves
Section: Chapter Questions
Problem 96P: Consider two waves y1(x,t) and y2(x,t) that are identical except for a phase shift propagating in...
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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 ( 100nt +
mm
%3D
X2 = 4.42 sin ( 100t
–2)
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 100rt ±
B cos 100nt, where A and B are numbers to be found.
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 ( 100nt + mm %3D X2 = 4.42 sin ( 100t –2) 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 100rt ± B cos 100nt, where A and B are numbers to be found.
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