Part 1: A support beam, within an industrial building, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the bear. The displacement caused by the vibrations can be modelled by the following equations, x₁ = 4.2 sin(100nt +0.59) mm x₂ = 6.1 sin(100mt-0.42) mm Your senior engineer asked you the followings: (a) State the amplitude, periodic time, frequency and phase angle (in degrees) for each of these waves.
Part 1: A support beam, within an industrial building, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the bear. The displacement caused by the vibrations can be modelled by the following equations, x₁ = 4.2 sin(100nt +0.59) mm x₂ = 6.1 sin(100mt-0.42) mm Your senior engineer asked you the followings: (a) State the amplitude, periodic time, frequency and phase angle (in degrees) for each of these waves.
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AAN EE
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Solving problems by relaung sinusordal wave and vector functions to their related
engineering applications. You also must solve the problems of differential and integral
calculus for your related works.
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Part 1:
A support beam, within an industrial building, is subjected to vibrations along its length;
emanating from two machines situated at opposite ends of the bear. The displacement
caused by the vibrations can be modelled by the following equations,
x₁ = 4.2 sin(100nt +0.59) mm
x₂ = 6.1 sin(100m - 0.42) mm
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Your senior engineer asked you the followings:
(a) State the amplitude, periodic time, frequency and phase angle (in degrees) for each
of these waves.
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(a) State the amplitude, periodic time, frequency and phase angle (in degrees) for each
of these waves.
(b) Determine the value of displacement when t-5.2 ms for each of these waves
(c) When does each vibration first reach to displacement 3.5 mm?
(d) How many seconds will it take for each machine's vibration to reach the maximum
displacement when the machines are switched on.
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(e) (i) Expand x, and x₂ by using the compound angle identities.
(ii) Express x₁ + x₂in a similar form by using your answer in parti(e) (i).
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