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 +) x2 = 4.42 sin ( 100nt – “) r 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 xz 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 ( x1 + x2)20 in terms of sinusoidal functions (sin, cos).
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 +) x2 = 4.42 sin ( 100nt – “) r 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 xz 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 ( x1 + x2)20 in terms of sinusoidal functions (sin, cos).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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