Develop a mathematical model and computer simulation

Reference no: EM132993359

Special Problem 1

Develop a mathematical model and computer simulation (Excel or MATLAB) to describe projectile mo- tion with air resistance. Details to help with the model and equation development at other similar websites.

Then using your model:

Calculate the minimum initial velocity (in mph) required to kick a 65 yard field goal. Note: The current record for the longest field goal in the NFL is 64 yards.
or

Calculate the minimum initial velocity (in mph) required to hit a 600 ft home run.

Assignment

1. Provide background and brief description of the problem.

2. Explain your mathematical model, including all assumptions.

3. Clearly state all inputs to your model and all outputs.

4. Present sufficient data (in graphical form?) and discuss your results.

5. Compare your result with air resistance to the case neglecting air resistance.

Communicate your results in a brief memo. A schematic, table, and/or figure will be useful to present your results. Attach all relevant calculations, programs, or spreadsheets in an appendix. Include references, properly formated.

Special Problem 2

A milling machine is supported on an elastic foundation as shown in the figure below. A external force, F (t), is applied to the machine during the metal cutting operation. In addition, the floor on which the machine is mounted is subjected to a harmonic disturbance, y(t), due to the operation of an unbalanced engine in the vincinity of the milling machine. The equation of vibration is given by

mx¨ + cx? + kx = cy? + ky + F (t)

If m = 5000 kg, c = 1 kN-s/m, k = 1 MN/m, y(t) = 2 sin(200πt) mm, and F (t) is given below.

Assignment

Specifically

1. Give a brief overview and description of the problem.

2. Derive the equation of motion. Explain your mathematical model, including all assumptions. Put the equation development in an appendix. Can be written by hand.

3. Clearly state all inputs to your model and all outputs.

4. Determine
(a) the displacement of the milling machine as a function of time for 0 ≤ t ≤ 10 s.
(b) the variation of velocity and acceleration of the milling machine over the period 0 ≤ t ≤ 10 s.

5. Present sufficient data (in graphical form?) and discuss your results.

Communicate your results in a brief memo. A figure will be useful to present your results. Attach all relevant calculations, programs, or spreadsheets in an appendix. Include references, properly formated.

Attachment:- Special Problem.rar

Reference no: EM132993359

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