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 2m 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 machin 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 100nt + B cos 100nt, where A and B are numbers to be found.

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 2m 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 machin 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 100nt + B cos 100nt, where A and B are numbers to be found.

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 (100zt +) m
*2 = 4.42 sin (100mt-
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 xz into the form A sin 100zt +
B cos 100nt, where A and B are numbers to be found.

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