A milling machine is supported on an elastic foundation as shown in the figure below

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 
mi-Eci+kx=4+ky+F(t) If m = 5000 kg, c = 1 kN-s/m, k = 1 MN/m, y(t) = 2 sin(200;rt) mm, and F(t) is given below. 
Column 

Overarm 
Arbor 

t.bte 
milling machine 
Arbor support Workpieee 
Flt). Newton 

U 
4 
external applied force 
t (sec) 
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. 
Grades will be based on the following: mathematical model development — 20%, computer implementation — 30%, results — 30%, and memo, i.e. presentation of results and discussion — 20%.