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Determining light beams and displacement

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A light beam composed of red and blue light is incident upon a rectangular glass plate. The light emerges into the air from point P as two separate beams

a. that are parallel, with the red beam displaced below the blue beam.
b. that are not parallel, with the blue beam displaced below the red beam.
c. that are not parallel, with the red beam displaced below the blue beam.
d. none of the above

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Solution Summary

This solution is provided in an attached .jpg file. It includes a diagram to further understanding of the problem and uses Snell's Law to calculate the solution.

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Assignment Question 3 in Applied Mechanics

Fig. Q3 shows a rigid light beam which is hinged at O to a wall. The beam carries a point mass of m at the free end. The beam is connected at its mid-point to a spring (stiffness k) which is also connected to a support that moves with a vertical motion y = Y sinwt. A damper (coefficient c) connects the mid-point of the beam to a fixed support.

(i) By taking moments about O of the forces acting on the beam show that an equation of motion can be obtained with the form

4mx + cx + kx = kY sin ωt

Please note that in the equation above the first x should have two dots above it and the second x should have one dot above it only. The reason why they haven't is because I am unsure how to type them in, my apologises.

where x is the displacement of the mid-point of the beam.

(ii) Determine the maximum value for w if the amplitude ratio of the x displacement (i.e. X) to Y is not to exceed 10%.

Take m = 2 kg; k = 6.25 kN/m; c = 45 Ns/m.
(The Answer to part (ii) is given as 87.8 rad/s)

Please could you respond to this question in its simplest form, with any additional notes for me to understand the process of the answer. I look forward to your reply. Many Thanks for your time and effort. Mr P Stones.
PS. I have also included an attachment of the question and sketch.

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