From 56aabf75f6dc7a25c1d54d6db0d09608ff9bac56 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Wed, 26 Apr 2017 17:22:47 -0400 Subject: [PATCH 1/2] added lecture 25 and corrected project numbers --- final_project/README.md | 8 ++++---- final_project/final_project.pdf | Bin 234524 -> 153104 bytes lecture_24/lecture_24.ipynb | 4 +++- lecture_24/octave-workspace | Bin 0 -> 153 bytes lecture_25/final_notes.pdf | Bin 0 -> 369941 bytes lecture_25/lecture_25.pdf | Bin 0 -> 324580 bytes myode.m | 7 +++++++ 7 files changed, 14 insertions(+), 5 deletions(-) create mode 100644 lecture_24/octave-workspace create mode 100755 lecture_25/final_notes.pdf create mode 100755 lecture_25/lecture_25.pdf create mode 100644 myode.m diff --git a/final_project/README.md b/final_project/README.md index cee3ee3..7a7b0ac 100644 --- a/final_project/README.md +++ b/final_project/README.md @@ -56,7 +56,7 @@ b. Use a Monte Carlo model to determine the mean and standard deviation for the maximum deflection $\delta x$ if b and h are normally distributed random variables with 0.1 % standard deviations at q=50 N/m. -3. Now use the central difference approximation to set up a system of equations for the +2. Now use the central difference approximation to set up a system of equations for the beam for q(x)=cst, P=0, and $\omega=0$. Use the boundary conditions with a numerical differentiation to determine the valuea of the end points @@ -71,7 +71,7 @@ differentiation to determine the valuea of the end points e. Comment on the results from the analytical and numerical approaches (if you used functions then provide help files, if you used scripts, then describe the steps used) -4. Now set up the system of equations using a central difference method if P>0 and +3. Now set up the system of equations using a central difference method if P>0 and $\omega=0$ a. set up the system of equations for 6 segments as a function of q and P @@ -83,7 +83,7 @@ $\omega=0$ d. solve a-c for q=1,10,20,30,50 and plot the numerical results of q vs $\delta x$ for P=0, 100, 200, 300 (4 lines, labeled as P=0,P=100,...) -5. Now set up an eigenvalue problem to solve for the natural frequencies of the simply +4. Now set up an eigenvalue problem to solve for the natural frequencies of the simply supported beam if P=0 and q=0. a. set up the system of equations for 6 segments @@ -96,7 +96,7 @@ supported beam if P=0 and q=0. e. Plot the shape of the beam for the first 3 natural frequencies -6. (Bonus 5pt) Create a function to return the system of equations for the eigenvalue +5. (Bonus 5pt) Create a function to return the system of equations for the eigenvalue problem as a function of P, if P>0. 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z1R9Uw{W+RQi`PTK`*Sp&#_EBdpJVwzLmaFggy-kzu^Qf=qwzFW4>X>}>Vd}7SU%9O z7OMxEP=mD(G@i!mfv literal 0 HcmV?d00001 diff --git a/myode.m b/myode.m new file mode 100644 index 0000000..cedefb6 --- /dev/null +++ b/myode.m @@ -0,0 +1,7 @@ +function dudt = myode(t,u) + x=u(1); + y=u(2); + dudt=zeros(2,1); + dudt(1)=0.1*x+0.3*x*y; + dudt(2)=0.1*x*y-2*y; +end \ No newline at end of file From d66829861382dc7c5c8638c66a851108104ffe10 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Wed, 26 Apr 2017 19:47:55 -0400 Subject: [PATCH 2/2] added competition #2 - Darts --- .../lecture_26-checkpoint.ipynb | 6 + lecture_26/compiled_data.csv | 233 ++++ lecture_26/lecture_26.ipynb | 1060 +++++++++++++++++ lecture_26/octave-workspace | Bin 0 -> 153 bytes 4 files changed, 1299 insertions(+) create mode 100644 lecture_26/.ipynb_checkpoints/lecture_26-checkpoint.ipynb create mode 100644 lecture_26/compiled_data.csv create mode 100644 lecture_26/lecture_26.ipynb create mode 100644 lecture_26/octave-workspace diff --git a/lecture_26/.ipynb_checkpoints/lecture_26-checkpoint.ipynb b/lecture_26/.ipynb_checkpoints/lecture_26-checkpoint.ipynb new file mode 100644 index 0000000..2fd6442 --- /dev/null +++ b/lecture_26/.ipynb_checkpoints/lecture_26-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_26/compiled_data.csv b/lecture_26/compiled_data.csv new file mode 100644 index 0000000..ea6a99a --- /dev/null +++ b/lecture_26/compiled_data.csv @@ -0,0 +1,233 @@ +7.8,62,1 +12.3,61,1 +5.2,35,1 +12.4,44,1 +5.2,294,1 +3.3,73,2 +1.4,30,2 +11,10,2 +6.3,39,3 +6.9,60,3 +6.3,100,3 +7.8,249,3 +3.3,282,3 +7,96,4 +3.9,186,4 +2.95,166,4 +8.6,262,4 +2.5,355,4 +20,155,5 +18.5,225,5 +14,45,5 +8.5,340,5 +5.25,95,5 +10,20,5 +6.5,62,5 +8.75,36,5 +3,190,5 +4.5,280,5 +2.25,62,6 +3.9,312,6 +9.3,36,6 +1.9,154,6 +7.3,115,6 +4.75,298,6 +4.6,306,7 +2.3,282,7 +10.1,138,7 +3.3,180,7 +8.5,242,7 +5,10,8 +2.5,350,8 +11,30,8 +4,272,8 +17,38,8 +3.75,85,9 +4.5,102,9 +1.36,118,9 +0.78,157,9 +3.41,198,9 +3,27,10 +1,88,10 +2,20,10 +2.5,155,10 +4.5,281,10 +1.5,75,10 +6.32,70,10 +2.85,135,10 +3.71,250,10 +5.45,60,10 +6.1,95,10 +5.5,92,11 +15,266,11 +12.5,14,11 +7,120,11 +4,132,11 +9,30,12 +5,90,12 +6,350,12 +8,330,12 +5,60,12 +3.81,140,12 +6.35,116,12 +0.635,88,12 +7.62,12,12 +1.27,180,12 +4.2,292,13 +0.8,165,13 +2.5,0,13 +6,43,13 +6.65,317,13 +1,0,13 +2.9,50,13 +7.4,302,13 +16.6,246,13 +2.4,234,13 +0.8,100,14 +3.6,62,14 +3.5,260,14 +4.4,168,14 +5.7,178,14 +3.6,143,14 +1.75,37,14 +1.95,62,14 +2.27,48,14 +4.26,69,14 +4,182,15 +5.8,100,15 +8.3,45,15 +10.2,30,15 +4,278,15 +3.81,120,16 +7.62,77,16 +1.59,212,16 +3.73,265,16 +4.84,259,16 +3.45,243,16 +2.1,186,16 +4.6,24,16 +0.7,343,16 +1.7,211,16 +12.4,33,17 +13.9,103,17 +4.5,307,17 +6.7,313,17 +11.4,328,17 +3,240,18 +4,330,18 +2,90,18 +3.5,315,18 +1,15,18 +4.6,98,19 +3.8,326,19 +3.4,184,19 +4,48,19 +2.6,83,19 +2.75,88,20 +1.33,93,20 +1.5,12,20 +3,280,20 +0.5,24,20 +1.2,130,21 +2.6,122,21 +0.8,296,21 +1.4,100,21 +1.2,290,21 +3,90,22 +2,30,22 +10,90,22 +3,15,22 +7,90,22 +3.3,170,23 +8.8,95,23 +8.1,71,23 +7.7,48,23 +9.6,301,23 +3,70,24 +1.2,10,24 +2.1,15,24 +6,260,24 +0.7,30,24 +12.5,10,25 +11,35,25 +7,320,25 +7.5,292,25 +3.5,134,25 +1,4,26 +2,3.9,26 +3,5.25,26 +4,3.2,26 +5,3,26 +4.5,27,27 +1.1,80,27 +2.6,155,27 +1.9,200,27 +2.8,325,27 +4.3,15,28 +7,145,28 +3.5,80,28 +9,210,28 +5.2,175,28 +1,54,29 +3.5,128,29 +4.5,140,29 +2,54,29 +11,274,29 +3.175,98,30 +1.5875,30,30 +3.175,282,30 +5.08,318,30 +10.795,316,30 +11.2,19,31 +14.5,232,31 +12.3,271,31 +16.9,120,31 +9,177,31 +7.4,276,32 +11.5,321,32 +1.5,36,32 +7.5,22,32 +10.1,66,32 +1.75,10,33 +2.5,123,33 +2,64,33 +1.8,271,33 +4,308,33 +4.5,39,34 +3.25,68,34 +2.5,282,34 +1.25,108,34 +2,122,34 +3.97,18,35 +8.29,196,35 +15.52,232,35 +4.79,93,35 +6.43,153,35 +7.5,74,36 +10.75,86,36 +3.5,96,36 +6.25,172,36 +5.5,38,36 +3.25,192,37 +4.5,88,37 +5,336,37 +4,176,37 +2.5,194,37 +1.5,73,38 +1.33,265,38 +2.15,92,38 +3.5,130,38 +0.9,65,38 +3.75,-2,39 +1.66,89,39 +5.43,76,39 +4.12,54,39 +6.87,63,39 +10,85,40 +9,30,40 +7,180,40 +4.3,22,40 +5.8,281,40 +2.9,1,40 +3.31,29,40 +1.5,10,40 diff --git a/lecture_26/lecture_26.ipynb b/lecture_26/lecture_26.ipynb new file mode 100644 index 0000000..dc43ec3 --- /dev/null +++ b/lecture_26/lecture_26.ipynb @@ -0,0 +1,1060 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%plot --format svg" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "setdefaults" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Monte Carlo Dart Challenge\n", + "\n", + "![Dart Challenge Figure](../HW2/projectile.png)\n", + "\n", + "In homework 2, you created `projectile.m`, that calculated the height of a dart based upon initial velocity and angle. \n", + "\n", + "For extra credit, we compiled data from 40 students. \n", + "\n", + "Now, we want to calculate the control that these students had over their dart-throwing. \n", + "\n", + "This is called an *inverse problem*. Given, a mean and standard deviation of velocity and angle, we can calculate the mean and standard deviation of the final dart height with a Monte-Carlo model, but we want to determine a reasonable estimate for the mean and standard deviation of these two parameters. \n", + "\n", + "This is an open-ended design problem, so you can choose to fix or vary the parameters at your own discretion. In HW3, we used 15 m/s as an initial velocity. This is a good starting point, but is it fixed? Its up to you to decide. \n", + "\n", + "You can use the Matlab/Octave command `hist` to plot the data and the Monte Carlo model results. And you can compare statistics with `mean` and `std`\n", + "\n", + "State your assumptions and provide documentation for your functions and scripts. \n", + "\n", + "### The goal of this challenge comes down to 3 parts:\n", + "\n", + "1. Determine a range of values for initial velocity and angle (intuition or analysis)\n", + "\n", + "2. Describe initial velocity and angle with random variables (normal distribution? completely random?)\n", + "\n", + "3. Show that your random variables produce the same ditribution of dart locations as our throwers\n", + "\n", + "### Submit your repository via the Google Form:\n", + "[https://goo.gl/forms/MwdfNWgj9UlHnRV83](https://goo.gl/forms/MwdfNWgj9UlHnRV83)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ans = 40\r\n" + ] + }, + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "Gnuplot\n", + "Produced by GNUPLOT 5.0 patchlevel 3 \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\t\n", + "\t \n", + "\t \n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\t\t\n", + "\t\n", + "\n", + "\n", + "\n", + "\n", + "\t\t\n", + "\t\t-20\n", + "\t\n", + "\n", 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