q2_cee3804_2011_sol

q2_cee3804_2011_sol - CEE 3804: Computer Applications in...

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Unformatted text preview: CEE 3804: Computer Applications in Civil Engineering Spring 2011 Quiz 2 Instructor: Trani Honor Code Pledge The information provided in this exam is my own work. I have not received information from another person while doing this exam. Solution Problem 1 (50 points) Show all your work as Screen Captures and Source Code. The differential equation to predict the angular acceleration ( )of a wrecking ball supported by a crane can be derived using a free body diagram shown in Figure 1. Figure 1. Free-Body Diagram for the Wrecking Ball. The fundamental equation of motion is: CEE 3804 Trani Page 1 of 14 F t = ma t = mg sin( ) Kl ma t = ml = mg sin( ) Kl = g sin( ) l K m where: K is the drag damping factor, is the angular position (in radians) between the vertical and the position of the rigid pendulum, m is the mass of the pendulum (kg) and l is the length of the pendulum (meters). The units of the equation are consistent to make the units of angular acceleration rad/s 2 . Task 1: Create a Matlab script and a function (i.e. two separate Iiles) that solve the differential equations of a runaway wrecking ball where the operator of the crane missed the target (usually a building in the process of being demolished). The solution to the differential equations should calculate the angular position ( ) and the angular speed ( ) as a function of time. Solve the differential equations for the following initial conditions: = and = 0.35 radians. n this solution assume the values of K to be 70, g=9.81 m/s 2 , l = 20 meters, and m =4,500 kg. __________ Matlab script _________________ Main File % Main fle to solve the equations oF motion % oF a wrecking ball and crane problem clear % Solution to a set oF equations oF the Form: % y(1) = angular speed (rad/s) % y(2) = angular displacement (rad) % % ydot(1) = - g * sin(y(2)) / l - K * y(1) /m; % ydot(2) = y(1) % % subject to initial conditions: % % y (t=0) = yo % % where: global K l m g % Defne Initial Conditions oF the Problem yo = [0 0.35]; % yo are the initial velocity and initial position CEE 3804 Trani Page 2 of 14 to = 0.0; % to is the initial time to solve this equation tf = 100; % tf is the Fnal time % deFne parameters K = 70 ; % damping constant m = 4500; % mass (kg) l = 20; % length in meters g = 9.81; % m/s-s tspan =[to tf]; [t,y] = ode15s( 'pendulum' ,tspan,yo); % call ODE solver % Plot the results of the numerical integration procedure Fgure plot(t,y(:,1)) xlabel( 'Time (seconds)' ) ylabel( 'Angular Speed (rad/s)' ) grid Fgure plot(t,y(:,2)) xlabel( 'Time (seconds)' ) ylabel( 'Angular Position (rad)' ) grid Fgure plot(y(:,1),y(:,2)) xlabel( 'Angular Speed (rad/s)' ) ylabel( 'Angular Position (rad)' ) grid ________________Function Pendulum ________________ % Two Frst-order DEQ to solve the wrecking ball + crane problem function ydot = pendulum(t,y) global K l m g % y(1) = angular speed (rad/s)...
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This note was uploaded on 01/01/2012 for the course CEE 3804 taught by Professor Aatrani during the Spring '07 term at Virginia Tech.

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q2_cee3804_2011_sol - CEE 3804: Computer Applications in...

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