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collar_mass.png
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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:

The spring is unstretched when x_C=0.5 m. 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=1/2*K *(DL)^2

where DL = 0.5 - sqrt(0.5^2+(0.5-x_C)^2) and K=30 N/m.

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)`