added HW4

tgr12001 · Feb 21, 2017 · 3780f0c36732e6e6d24aca6beb2e1b1dbcfe90a1 · 3780f0c
1 parent 07507da
commit 3780f0c36732e6e6d24aca6beb2e1b1dbcfe90a1
Unified Split

Showing with 307 additions and 0 deletions.

+37 −0 HW4/README.md

+270 −0 HW4/collar_mass.svg
diff --git a/HW4/README.md b/HW4/README.md
@@ -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.
diff --git a/HW4/collar_mass.svg b/HW4/collar_mass.svg
@@ -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>