Assignment

Use MATLAB to solve each problem by writing script files; copy and paste the script file AND the results in the Command Windowand/or plot in the Figure Windowto a WORD document that has your name and section in the headers of each page and the page number in each footer. Edit the output to remove extra lines and empty spaces. The script files SHOULD have comments for easy readability; take a print out of the Word file andstaple before submission.

1. Plot the function y = 10(1-e^-x/4) over the interval 0 £ x £x_max, using a while loop to determine the value of x_max such that y(x_max) = 9.8. The variable y represents force in Newtons, and the variable x represents time in seconds. Include title, grid, and axis labels.

2. A weight is supported by two cables anchored a distance D apart as shown.

The cable length L_AB is given, but the length L_AC is to be selected. Each cable can support a maximum tension force equal to W. For the weight to remain stationary, the total horizontal force and the total vertical force must each be zero. This principle gives the equations

          -T_AB cosq + T_AC cos f = 0
           T_AB sinq + T_AC sin f = W

W can solve these equations for the tension forces T_AB and T_AC if we know the angles q and f. From the law of cosines

                                            θ = cos^-1 [(D² + L³_AB - L²_AC) / 2DL_AB]
From the law of sines              Φ = sin^-1 (L_AB sinθ / L_AC)

For the given values D = 6 feet, L_AB = 3 feet, and W = 2000 pounds, use a loop in MATLAB to find L_ACmin, the shortest length L_AC we can use without T_AB or T_AC exceeding 2000 pounds. Note that the largest L_AC can be is 6.7 feet (which corresponds to q = 90°). Plot the tension forces T_AB and T_AC on the same graph versus L_AC for L_ACmin£ L_AC£ 6.7.

3. An ideal diode blocks the flow of current in the direction opposite that of the diode's arrow symbol. It can be used to make a half-wave rectifier as shown.

For the ideal diode, the voltage v_L across the load R_L is given by

               v_L = v_Sif  v_S> 0
                   = 0      if  v_S£ 0

For a non- ideal (silicon) diode, the voltage v_L is given by

               v_L = v_S-0.6    if  v_S> 0.6
                   = 0      if  v_S£ 0.6

Suppose the supply voltage is v_s(t) = 3e^-t/3 sin(pt) volts, where time t is in seconds. Write a MATLAB program to plot the voltage  v_L versus t for both ideal and non-ideal cases  and the voltage v_S versus t for 0 £ t £ 10 on the same axes.

4. Write a user-defined MATLAB function that calculates a student's final grade in a course using the scores from three midterm exams, a final exam, and six homework assignments. The midterms are graded on a scale from 0 to 100, and are each 15% of the final grade. The final exam is graded on a scale from 0 to 100, and is 45% of the final grade. The six homework assignments are graded each on a scale from 0 to 10. The homework assignments together are 10% of the final grade.

For the function name and arguments use g=fgrade(R). The input argument R is a matrix in which the elements in each row are the grades of one student. The first six columns are the homework grades (numbers between 0 to 10), the next three columns are the midterm grades (numbers between 0 to 100), and the last column is the final grade (a number between 0 to 100). The output from the function, g, is a column vector with the final grades for the course. Each row has the final grade of the student with the final grades in the corresponding row of the matrix R. 

The function can be used to calculate the grades of any number of students. For one student matrix R has one row. Use the function in the following cases:

a) Use the Command Window to calculate the grade of one student with the following grades:

(8, 9, 6, 10, 9, 8, 76, 86, 91, 80).

b) Write a program in a script file. The program asks the user to enter the student's grades in an array (each student a row). The program then calculates the final grades by using the function fgrade. Run the script file to calculate the grades of the following four students:   

Student A:  8, 10, 6, 9,10,9, 91, 71, 81, 85.
Student B:  5, 5, 6, 1, 8, 6, 59, 72, 66, 59.
Student C:  6, 8, 10, 4, 5, 9, 55, 65, 75, 78.
Student D:  7, 7, 8, 8, 9, 8, 83, 82, 81, 84.