HW4

due 3/1/17 by 11:59pm

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

The spring is unstretched when x_C=0.5 m. The potential energy due to gravity is:

PE_g=m x_Cgsin(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

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

#Part 1 theta = 0; f =@(x_C) collar_potential_energy(x_C,theta); [x,fx,ea,iter]=goldmin(f,0,0.5,0.0000001,1000); x fx

#Part 2 theta(1) =0;

for i=1:91; f =@(x_C) collar_potential_energy(x_C,theta(i)); [x(i),fx(i),ea(i),iter(i)]=goldmin(f,0,0.5,1e-6,1000); theta(i+1) = theta(i) +1; end

plot(theta(1:91),x(1:91));