Skip to content
Permalink
Browse files

added HW4

  • Loading branch information
rcc02007 committed Feb 21, 2017
1 parent 07507da commit 3780f0c36732e6e6d24aca6beb2e1b1dbcfe90a1
Showing with 307 additions and 0 deletions.
  1. +37 −0 HW4/README.md
  2. +270 −0 HW4/collar_mass.svg
@@ -0,0 +1,37 @@
# 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.
@@ -0,0 +1,270 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->

<svg
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:cc="http://creativecommons.org/ns#"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
width="3in"
height="2in"
viewBox="0 0 270 180"
id="svg4226"
version="1.1"
inkscape:version="0.91 r13725"
sodipodi:docname="collar_mass.svg">
<defs
id="defs4228">
<marker
inkscape:stockid="Arrow2Mend"
orient="auto"
refY="0.0"
refX="0.0"
id="Arrow2Mend"
style="overflow:visible;"
inkscape:isstock="true">
<path
id="path4186"
style="fill-rule:evenodd;stroke-width:0.625;stroke-linejoin:round;stroke:#000000;stroke-opacity:1;fill:#000000;fill-opacity:1"
d="M 8.7185878,4.0337352 L -2.2072895,0.016013256 L 8.7185884,-4.0017078 C 6.9730900,-1.6296469 6.9831476,1.6157441 8.7185878,4.0337352 z "
transform="scale(0.6) rotate(180) translate(0,0)" />
</marker>
<marker
inkscape:stockid="Arrow1Mend"
orient="auto"
refY="0.0"
refX="0.0"
id="marker4761"
style="overflow:visible;"
inkscape:isstock="true">
<path
id="path4763"
d="M 0.0,0.0 L 5.0,-5.0 L -12.5,0.0 L 5.0,5.0 L 0.0,0.0 z "
style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1;fill:#000000;fill-opacity:1"
transform="scale(0.4) rotate(180) translate(10,0)" />
</marker>
<marker
inkscape:isstock="true"
style="overflow:visible;"
id="marker4709"
refX="0.0"
refY="0.0"
orient="auto"
inkscape:stockid="Arrow1Mend">
<path
transform="scale(0.4) rotate(180) translate(10,0)"
style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1;fill:#000000;fill-opacity:1"
d="M 0.0,0.0 L 5.0,-5.0 L -12.5,0.0 L 5.0,5.0 L 0.0,0.0 z "
id="path4711" />
</marker>
<marker
inkscape:isstock="true"
style="overflow:visible;"
id="marker4651"
refX="0.0"
refY="0.0"
orient="auto"
inkscape:stockid="Arrow1Mend">
<path
transform="scale(0.4) rotate(180) translate(10,0)"
style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1;fill:#000000;fill-opacity:1"
d="M 0.0,0.0 L 5.0,-5.0 L -12.5,0.0 L 5.0,5.0 L 0.0,0.0 z "
id="path4653" />
</marker>
<marker
inkscape:isstock="true"
style="overflow:visible;"
id="marker4599"
refX="0.0"
refY="0.0"
orient="auto"
inkscape:stockid="Arrow1Mend">
<path
transform="scale(0.4) rotate(180) translate(10,0)"
style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1;fill:#000000;fill-opacity:1"
d="M 0.0,0.0 L 5.0,-5.0 L -12.5,0.0 L 5.0,5.0 L 0.0,0.0 z "
id="path4601" />
</marker>
<marker
inkscape:stockid="Arrow2Mstart"
orient="auto"
refY="0.0"
refX="0.0"
id="Arrow2Mstart"
style="overflow:visible"
inkscape:isstock="true">
<path
id="path4183"
style="fill-rule:evenodd;stroke-width:0.625;stroke-linejoin:round;stroke:#000000;stroke-opacity:1;fill:#000000;fill-opacity:1"
d="M 8.7185878,4.0337352 L -2.2072895,0.016013256 L 8.7185884,-4.0017078 C 6.9730900,-1.6296469 6.9831476,1.6157441 8.7185878,4.0337352 z "
transform="scale(0.6) translate(0,0)" />
</marker>
<marker
inkscape:stockid="Arrow1Mend"
orient="auto"
refY="0.0"
refX="0.0"
id="Arrow1Mend"
style="overflow:visible;"
inkscape:isstock="true"
inkscape:collect="always">
<path
id="path4168"
d="M 0.0,0.0 L 5.0,-5.0 L -12.5,0.0 L 5.0,5.0 L 0.0,0.0 z "
style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1;fill:#000000;fill-opacity:1"
transform="scale(0.4) rotate(180) translate(10,0)" />
</marker>
</defs>
<sodipodi:namedview
id="base"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:pageopacity="0.0"
inkscape:pageshadow="2"
inkscape:zoom="3.3611111"
inkscape:cx="120.9995"
inkscape:cy="105.14521"
inkscape:document-units="px"
inkscape:current-layer="layer1"
showgrid="false"
units="in"
inkscape:window-width="2560"
inkscape:window-height="1379"
inkscape:window-x="1920"
inkscape:window-y="27"
inkscape:window-maximized="1" />
<metadata
id="metadata4231">
<rdf:RDF>
<cc:Work
rdf:about="">
<dc:format>image/svg+xml</dc:format>
<dc:type
rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
<dc:title></dc:title>
</cc:Work>
</rdf:RDF>
</metadata>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
transform="translate(0,-872.36215)">
<rect
style="opacity:1;fill:#878787;fill-opacity:1;fill-rule:nonzero;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
id="rect4151"
width="252.7438"
height="10.413223"
x="-489.34341"
y="916.44434"
rx="0"
ry="0"
transform="matrix(0.86525768,-0.50132739,0.50132739,0.86525768,0,0)" />
<rect
style="opacity:1;fill:#878787;fill-opacity:1;fill-rule:nonzero;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
id="rect4149"
width="36.743797"
height="20.975229"
x="334.47769"
y="-935.25085"
ry="1.9338843"
rx="3.8677685"
transform="matrix(-0.87030691,0.49250978,-0.49250978,-0.87030691,0,0)" />
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-end:url(#Arrow1Mend)"
d="M 38.380165,1042.6927 131.20661,989.13901"
id="path4153"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cc" />
<text
xml:space="preserve"
style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
x="100.26447"
y="1023.6514"
id="text4501"
sodipodi:linespacing="125%"><tspan
sodipodi:role="line"
id="tspan4503"
x="100.26447"
y="1023.6514"
style="font-size:17.5px">x<tspan
style="font-size:64.99999762%;baseline-shift:sub"
id="tspan4507">c</tspan></tspan></text>
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 87.192722,890.41573 5.789029,6.4627 c 0,0 11.268949,1.73825 11.459939,6.05433 0.15694,3.5463 -8.939835,5.78682 -8.939835,5.78682 0,0 17.602265,1.25928 18.153375,7.82562 0.29688,3.53732 -8.93984,5.78682 -8.93984,5.78682 0,0 17.60226,1.25927 18.15336,7.82561 0.2969,3.53734 -8.93983,5.78682 -8.93983,5.78682 0,0 17.60225,1.25928 18.15337,7.82562 0.29689,3.53733 -8.93984,5.78682 -8.93984,5.78682 0,0 11.36441,-2.94841 13.5466,1.0194 1.10746,2.01365 -3.24487,6.08294 -3.24487,6.08294 l 8.94372,13.2138"
id="path4509"
inkscape:connector-curvature="0"
sodipodi:nodetypes="ccscscscscscc" />
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="M 77.652893,895.71752 100.41322,881.88281"
id="path4511"
inkscape:connector-curvature="0" />
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 78.099174,894.97372 1.190082,-10.26446"
id="path4513"
inkscape:connector-curvature="0" />
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 84.396695,891.64314 1.190082,-10.26445"
id="path4513-6"
inkscape:connector-curvature="0" />
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="M 91.586777,887.19685 92.776859,876.9324"
id="path4513-2"
inkscape:connector-curvature="0" />
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 99.586777,883.19685 1.190083,-10.26444"
id="path4513-2-9"
inkscape:connector-curvature="0" />
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 129.12397,996.87455 c 7.50466,13.72735 7.9919,31.61045 -0.29752,45.83475"
id="path4551"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cc" />
<text
xml:space="preserve"
style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
x="141.0248"
y="1029.7505"
id="text4553"
sodipodi:linespacing="125%"><tspan
sodipodi:role="line"
id="tspan4555"
x="141.0248"
y="1029.7505"
style="font-size:17.5px">𝝷</tspan></text>
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 38.082645,1042.6927 190.710745,0"
id="path4557"
inkscape:connector-curvature="0" />
<path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;marker-start:url(#Arrow2Mstart);marker-end:url(#Arrow2Mend)"
d="m 99.966942,883.51918 51.619838,80.62809"
id="path4559"
inkscape:connector-curvature="0" />
<text
xml:space="preserve"
style="font-style:normal;font-weight:normal;font-size:17.5px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
x="136.41322"
y="916.69275"
id="text4881"
sodipodi:linespacing="125%"><tspan
sodipodi:role="line"
id="tspan4883"
x="136.41322"
y="916.69275">L<tspan
style="font-size:65%;baseline-shift:sub"
id="tspan4885">0</tspan>=0.5m</tspan></text>
</g>
</svg>

0 comments on commit 3780f0c

Please sign in to comment.
You can’t perform that action at this time.