Write the equations in matrix form and use matlab matrix to

Question

Assignment -

Write one MATLAB program and make use of the MATLAB's menu command that creates three (3) interactive menu buttons to solve the following 3 problems.

Problem 1: A truss is a structure made of members joined at their ends. For the truss shown in the figure, the force in the 9 members are determined by solving the following system of 9 equations (attached):

Write the equations in matrix form and use MATLAB matrix to determine the forces in the members. A positive force means tensile force and a negative force means compressive force. Display the results in a table where the first column displays the member name, the second column displays the corresponding force, and the third column shows the type of tensile or compressive force.\

Problem 2: A ball thrown up falls back to the floor and bounces many times. For a ball thrown up in the direction shown in the figure, the position of the ball as a function of time is given by:

x = v_xt    y = v_yt    z = v_zt- ½gt²

The velocities in the x and y directions are constants throughout the motion and are given by v_x = v₀sin(θ)cos(α) and v_y = v₀sin(θ)sin(α). In the vertical z direction the initial velocity is v_z = v₀cos(θ), and when the ball impacts the floor its rebound velocity is 0.8 of the vertical velocity at the start of the previous bounce. The time between bounces is given by t_b = (2v_z)/g, where v_z is the vertical component of the velocity at the start of the bounce. Make a 3-D plot (shown in the figure) that shows the trajectory of the ball during the first five bounces. Take v₀ = 20 m/s, θ = 30^o, α = 25^o, and g = 9.81 m/s².

Problem 3: The flow Q (m³/s) in a rectangular channel is given by the Manning's equation:

Q = kdw/n(wd/w+2d)^2/3√S

where d is the depth of water (m), w is the width of the channel (m), S is the slope of the channel (m/m), n is the roughness coefficient of the channel walls, and k is a conversion constant (equal to 1 when the units above are used). Make a 3-D plot of Q (z axis) as a function of w (x axis) for 0 ≤ w ≤ 8 m, and a function of d (y-axis) for 0 ≤ d ≤ 4 m. Assume n = 0.05 and S = 0.001 m/m.

Attachment:- Assignment File.rar