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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 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

    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)

  2. Commit your changes to your repository. Sync your local repository with github.

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