Question

The equations of motion for a certain mechanical system with two degrees of freedom, can be written as a pair of coupled, second-order, differential equations: (M + m)x - 1/2 mL theta^2 sin(theta) + 1/2 mL theta cos(theta) + k(x - L_0) = 0 1/3 mL^2 theta + 1/2 mLx cos(theta) + 1/2 mgLsin(theta) = 0 We can rewrite them in matrix form, A*qdd - b, to be solved simultaneously: [M + m 1/2 mL cos theta 1/2 mL cos theta 1/3 mL^2][x theta] = [1/2 mL theta^2 sin theta - k(x - L_0) -1/2 mg mgL sin theta] Write a MATLAB program that: prompts the user to enter M, m, L, k, L_0, and g, initial x, theta, x, and theta, and duration, provides default values of 1 kg, 1 kg, 1 m, 10 N/m, 1 m, 9.81 m/s^2, 0 m, 0 rad, 0 m/s, 0 rad/s, and 5 seconds so that the user can run the program without typing any values. For example: m - str2num(input('Enter mass m in kg (1): ', 's')); if isempty(m), m = 1; end % if nothing entered, supply default uses ode45() to solve these equations simultaneously, and qdd = A\B; % calculate accelerations iron inv(A)*B, but faster graphs both x and theta as functions of time on a single plot with appropriate axes labels that include units, a legend, and a title the with all constants, parameters, and initial condition with units and formatted appropriately. Submit the following: your MATLAB program formatted in 10 pt courier font 1 plot showing the motion with the default values 1 plot showing noticeably different motion with a different set of values Exercise 2 Assemble a square matrix with the following algorithm: First, define the matrix with all zeros.

Answer 1

Solution:

Code: