Assignment

Use MATLAB to solve each problem by writing script files; copy and paste the script file AND the results in the Command Window to 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 as shown in the solutions to the assignments 1 and 2. The script files SHOULD have comments for easy readability; take a print out of the file and the print out of the plot, andstaple before submission.

1. Plot the function f(x) = sin (2x) cos² (0.5x) and its derivative, both on the same plot, for -π ≤ x ≤ 2π. Plot the function with a solid line and he derivative with a dashed line. Add a legend and Label the axes.

2. The data for a tension test on a steel bar appears in the following table. The elongation is the change in the bar's length. Plot the tension force versus the elongation. Be sure to label the parts of the curve that correspond to increasing and decreasing tension. Label the axes and include the title. Use continuous line for one plot and dot-dash line for the other. Use different colors for each.

3. The following functions describe the oscillations in electrical circuits and the vibrations of machines and structures. Plot these functions on the same plot. Label them clearly. Label the axes and include the title. Use continuous line for one plot and dot-dash line for the other. Use different colors for each.

x(t) = 10e^-0.5t sin(3t+2)
y(t) = 7e^-0.4t cos(5t-3)

4. Semi-log plots are very useful in many practical applications. One such application is the frequency-response characteristic of an electrical filter. These filters allow signals of specified frequencies while preventing signals outside the range. In a semilog plot, one axis is linear while the other axis is logarithmic. The frequency-response characteristics are also called Bode plots. Given a function, F(ω), Bode magnitude plot is 20*log₁₀|F(ω)| versus log₁₀ω; ω is the radian frequency in rad/s. Bode phase plot is θ(ω) versus log₁₀ω, where θ(ω) is the phase angle, in degrees, of the function F(ω). Both are semi-log plots since the magnitude and the phase angle values are linear while the radian frequency is logarithmic. Radian frequency values vary over a wide range. As a result they will not fit on linear scale. In this problem, assume that F(ω) = 1 / (1 + 0.1iω). Let the radian frequency ω vary from 1 rad/s to 100 rad/s. Draw the Bode plots using MATLAB. Plot them one below the other on the same page. (Use subplot command). Label the axes, include title and grid.

5. The Orbit of the planet Mercury around the sun can be approximated by the equation r = (3.44 x 107) / (1 - 0.206 cos θ) miles. Make a plot of the orbit.