% Define symbolic variables syms theta mu mg L N theta_dot_dot theta_dot_squared % Define theta_dot_squared | theta_dot_squared ((12*g)/L) - ((12*g*cos(theta))/(L)) + 3*(cos(theta))^2; % Define the expression for theta_dot_dot theta_dot_dot = (-(6*g* (sin(theta) - mu*cos(theta))))/L - (cos(theta) * (sin(theta) % Define N * N = -(m*L)/2 (theta_dot_dot *sin(theta)) * sin(theta)) - (m*L)/2. (mL)/2 (theta_dot_squared *cos(theta)) + mg; % Define the equation for mu: mu * N = (m*L)/2* (theta_dot_dot *cos(theta) theta_dot_squared * - mu_eqn = mu * N == (m*L)/2 * (theta_dot_dot * cos (theta) - theta_dot_squared * sin(theta)); cos(theta) mu*cos(theta)) * (9* cos(theta)^2 + (36*g)/L - (36*g*cos(theta))/L))/(3* sin(theta)*(sin(theta) mu*cos(theta)) 1); - sin(theta))
% Define symbolic variables syms theta mu mg L N theta_dot_dot theta_dot_squared % Define theta_dot_squared | theta_dot_squared ((12*g)/L) - ((12*g*cos(theta))/(L)) + 3*(cos(theta))^2; % Define the expression for theta_dot_dot theta_dot_dot = (-(6*g* (sin(theta) - mu*cos(theta))))/L - (cos(theta) * (sin(theta) % Define N * N = -(m*L)/2 (theta_dot_dot *sin(theta)) * sin(theta)) - (m*L)/2. (mL)/2 (theta_dot_squared *cos(theta)) + mg; % Define the equation for mu: mu * N = (m*L)/2* (theta_dot_dot *cos(theta) theta_dot_squared * - mu_eqn = mu * N == (m*L)/2 * (theta_dot_dot * cos (theta) - theta_dot_squared * sin(theta)); cos(theta) mu*cos(theta)) * (9* cos(theta)^2 + (36*g)/L - (36*g*cos(theta))/L))/(3* sin(theta)*(sin(theta) mu*cos(theta)) 1); - sin(theta))
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter7: Arrays
Section: Chapter Questions
Problem 9PP: (Data processing) Your professor has asked you to write a C++ program that determines grades at the...
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Question
Using MATLAB symbolic toolbox, given these 3 equations, how would you solve for mu = function(theta), making sure that there are no mu's on the right hand side, making sure theta-dot-dot, theta-dot-squared- and N aren't in the final answer either.

Transcribed Image Text:% Define symbolic variables
syms theta mu mg L N theta_dot_dot theta_dot_squared
% Define theta_dot_squared |
theta_dot_squared
((12*g)/L) - ((12*g*cos(theta))/(L)) + 3*(cos(theta))^2;
% Define the expression for theta_dot_dot
theta_dot_dot = (-(6*g* (sin(theta) - mu*cos(theta))))/L - (cos(theta) * (sin(theta)
% Define N
*
N = -(m*L)/2 (theta_dot_dot *sin(theta))
* sin(theta)) - (m*L)/2.
(mL)/2 (theta_dot_squared *cos(theta)) + mg;
% Define the equation for mu: mu * N = (m*L)/2* (theta_dot_dot *cos(theta) theta_dot_squared *
-
mu_eqn = mu * N == (m*L)/2 * (theta_dot_dot * cos (theta) - theta_dot_squared * sin(theta));
cos(theta)
mu*cos(theta)) * (9* cos(theta)^2 + (36*g)/L - (36*g*cos(theta))/L))/(3* sin(theta)*(sin(theta)
mu*cos(theta)) 1);
-
sin(theta))
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