A moving component is subjected to vibrations along its length, emanating from two machines situated at...

 

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A moving component is subjected to vibrations along its length, emanating from two machines situated at opposite ends. The displacement caused by the vibrations can be modelled by the following equations: x₁ A₁ sin B₁лt + = 2π 8 X2 A2 sin B2л - 27 You have been asked to solve the following equations: (a) State the amplitude, phase angle, 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) Use the compound angle formulae to expand each of x and x2 into the form Asin100πt ± Bcos100лt, where A and B are numbers to be found. (d) Add the two displacements: x1 + x2 and convert it into the equivalent form Rsin(100πta). And express it in the form Asin100лt± Bсos100лt, where A and B are numbers to be found. (e) Using appropriate spreadsheet software, copy and complete the following table of values: X1 X2 0 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.01 1 3 5 7 9 1 3 5 7 9 A moving component is subjected to vibrations along its length, emanating from two machines situated at opposite ends. The displacement caused by the vibrations can be modelled by the following equations: x₁ A₁ sin B₁лt + = 2π 8 X2 A2 sin B2л - 27 You have been asked to solve the following equations: (a) State the amplitude, phase angle, 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) Use the compound angle formulae to expand each of x and x2 into the form Asin100πt ± Bcos100лt, where A and B are numbers to be found. (d) Add the two displacements: x1 + x2 and convert it into the equivalent form Rsin(100πta). And express it in the form Asin100лt± Bсos100лt, where A and B are numbers to be found. (e) Using appropriate spreadsheet software, copy and complete the following table of values: X1 X2 0 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.01 1 3 5 7 9 1 3 5 7 9

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a State the amplitude phase angle frequency and periodic time of each of these waves For the first w... View the full answer