Homework Assignment #2

• Obtain an input/output model for the mechanical system shown in problem 3.7 of the text. In your model, the input will be the applied torque Tm, and the output will be the motion of the mass, measured by the deflection x1 (instead of velocity v1). In this problem, we assume that the pulley (J,r2,Omega2) is first rotated such that the cable is "very stiff in tension". The torque required to tension the cable is not to be included in Tm. The deflection x1 of the mass is measured from the position of static deflection required to place the cable in "very stiff tension". Classify the model as to linearity/nonlinearity and order.
• Place the following set of equations
  x1+3*x2+x3=2
  x1-2*x2+x3=3
  2*x1+x2+3*x3=1
  in the matrix format Ax=b. Write down A, b, and state their dimensions. Using Matlab, write an "m file" that will calculate the solution x=A^(-1)b. Attach copies of the m file and the results of running the program.
• Using Matlab, write an "m file" that will i) define a row vector x consisting of 150 evenly spaced elements ranging from 20-40, ii) calculate a row vector y=22*x-3*x^2 using element by element operations, and iii) plot y versus x with axis labels. Attach copies of the m file and the results of running the program.
• Using Matlab, write a function that has as its input argument yin a row vector of dimension 4, and a corresponding output yout consisting of a column vector of dimension 4. In the function, compute
  yout(1)=yin(2)
  yout(2)=yin(1)^2-yin(1)
  yout(3)=yin(4)
  yout(4)=yin(2)-3*yin(1)
  Attach copies of the m file and the results of running the function with yin=[1 2 3 4].

Solutions in ME313_HW2.pdf

Assignment Due Monday September 28 1998.