added HW4

HW4/README.md

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+# Homework #3
+## due 3/1/17 by 11:59pm
+
+
+1. Use your repository 'roots_and_optimization'. Document all the HW4 work under the
+heading `# Homework #4` in your `README.md` file
+
+    a. Create a function called 'collar_potential_energy' that computes the total
+    potential energy of a collar connected to a spring and sliding on a rod. As shown in
+    the figure given a position, xc, and angle, theta:
+
+    ![Collar-mass on an inclined rod](collar_mass.svg)
+
+    The spring is unstretched when $x_{C}=0.5$. The potential energy due to gravity is:
+
+    $PE_{g}=m x_{C}g\sin\theta$
+
+    where m=0.5 kg, and g is the acceleration due to gravity, 
+
+    and the potential energy due to the spring is:
+
+    $PE_{s}=1/2K (\Delta L)^{2}$
+
+    where $\Delta L = 0.5 - \sqrt{0.5^{2}+(0.5-x_{C})^{2}}$
+
+    b. Use the `goldmin.m` function to solve for the minimum potential energy at xc when
+    theta=0. *create an anonymous function with `@(x) collar_potential_energy(x,theta)` in
+    the input for goldmin. Be sure to include the script that solves for xc*
+
+    c. Create a for-loop that solves for the minimum potential energy position, xc, at a
+    given angle, theta, for theta = 0..90 degrees. 
+
+    d. Include a plot of xc vs theta. `plot(theta,xc)` with
+
+    `![Steady-state position of collar on rod at angle theta](plot.png)`
+
+3. Commit your changes to your repository. Sync your local repository with github.