Task 4A support beam is subjected to vibrations along its length, emanating from two machinessituated at opposite ends of the beam. The displacement caused by the vibrations can bemodelled by the following equations,x1 = 3.75 sin ( 100nt +mmx2 = 4.42 sin ( 100nt – ),mma. 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 machineto 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 x2 into the form A sin 100t ±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 ofR sin(100tbt +a).f. Express the 10th term of ( x, + x2)20 in terms of sinusoidal functions (sin, cos).g. Using appropriate spreadsheet software, copy and complete the following table of values:t0.000 | 0.002 | 0.004 | 0.006 | 0.008 | 0.010 | 0.012 | 0.014 | 0.016 | 0.018 | 0.020X1| x2h. Plot the graphs of x1 and x2 on the same axes using any suitable computer package.Extend your table to include x, + x2 , x1 – x2 , and plot these graphs on the same axes asthe previous two. State the amplitude and frequency of the new wave. Repeat for e and f.Using your answers from parts g and h, what conclusions can be drawn about x1 + x2and the two methods that were used to obtain this information?i.

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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 x2 = 4.42 sin (100t – ) m 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?

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 x2 = 4.42 sin (100t – ) m 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?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Stretched string

A stretched string is a wire which is made up of any metal that must have a larger length compared to its thickness. The ends of the wire are fixed, and when they oscillate or are plucked, it produces two reflected transverse waves of the same frequency and same amplitude. The waves or pulses are traveling in alternate directions and superimpose with one another. This waveform is named standing or stationary waves.

Question

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
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?
d. Use the compound angle formulae to expand x, and x2 into the form A sin 100t ±
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(100tbt +a).
f. Express the 10th term of ( x, + x2)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
h. Plot the graphs of x1 and x2 on the same axes using any suitable computer package.
Extend your table to include x, + 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.
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?
i.

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