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    5 - MatLab Tutorial

    Uploaded by

    Simay Oğuzkurt
    The document provides 3 MATLAB tutorials: 1. Generates a plot of the charge variation over time for an RLC circuit based on given parameters. 2. Generates a plot of the standard normal probability density function from z=-5 to 5, labeling the axes as frequency and z. 3. Generates a single plot showing the trajectory of an object based on its initial angle, velocity, and height for varying horizontal distances, with trajectories for different initial angles distinguished by a legend.

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    5 - MatLab Tutorial

    Uploaded by

    Simay Oğuzkurt
    63 views3 pages
    The document provides 3 MATLAB tutorials: 1. Generates a plot of the charge variation over time for an RLC circuit based on given parameters. 2. Generates a plot of the standard normal probability density function from z=-5 to 5, labeling the axes as frequency and z. 3. Generates a single plot showing the trajectory of an object based on its initial angle, velocity, and height for varying horizontal distances, with trajectories for different initial angles distinguished by a legend.

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    The document provides 3 MATLAB tutorials: 1. Generates a plot of the charge variation over time for an RLC circuit based on given parameters. 2. Generates a plot of the standard normal probability density function from z=-5 to 5, labeling the axes as frequency and z. 3. Generates a single plot showing the trajectory of an object based on its initial angle, velocity, and height for varying horizontal distances, with trajectories for different initial angles distinguished by a legend.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    63 views3 pages

    5 - MatLab Tutorial

    Uploaded by

    Simay Oğuzkurt
    The document provides 3 MATLAB tutorials: 1. Generates a plot of the charge variation over time for an RLC circuit based on given parameters. 2. Generates a plot of the standard normal probability density function from z=-5 to 5, labeling the axes as frequency and z. 3. Generates a single plot showing the trajectory of an object based on its initial angle, velocity, and height for varying horizontal distances, with trajectories for different initial angles distinguished by a legend.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    TUTORIAL

    1. A simple electric circuit consisting of a resistor, a capacitor, and an inductor is given in


    below figure.

    The charge on the capacitor q(t) as a function of time can be computed as

    1 𝑅 2
    𝑞 = 𝑞0 𝑒 −𝑅𝑡/(2𝐿)
    𝑐𝑜𝑠 [ √ − ( ) 𝑡]
    𝐿𝐶 2𝐿
    where t = time, q0 = the initial charge, R = the resistance, L = inductance, and C =
    capacitance. Use MATLAB to generate a plot of this function from t = 0 to 0.8, given that
    q0 = 10, R = 60, L = 9, and C = 0.00005. (You can take the increment as 0.1 for time). Axis
    labels should be bold and 12 points. Title should be bold and 14 points. Also there should
    be a legend on the plot.

    %% T(1)
    % givens
    q0 = 10;
    R = 60;
    L = 9;
    C = 0.00005;

    % time = 0 to 0.8; increment can be 0.1


    t = 0:0.1:0.8;

    % charge within time is


    q = q0*exp((-R.*t)/2*L).*cos(sqrt((1/L*C)-(((R/2*L)^2).*t)));

    %% plotting
    h = plot(t,q, 'LineWidth', 1.5, 'Color', 'c', 'Marker', 'h', 'MarkerSize', 12,
    'MarkerFaceColor', 'k', 'MarkerEdgeColor', 'c');
    title('Charge Variations within Time', 'FontSize', 14, 'FontWeight', 'bold');
    xlabel('Time', 'FontSize', 12, 'FontWeight', 'bold');
    ylabel('Charge', 'FontSize', 12, 'FontWeight', 'bold');
    legend('q');

    2. The standard normal probability density function is a bell-shaped curve that can be
    represented as

    1 −𝑧 2⁄
    𝑓(𝑧) = 𝑒 2
    √2𝜋

    Use MATLAB to generate a plot of this function from z = -5 to 5. Label the ordinate as
    frequency and the abscissa as z.

    %% T(2)
    % givens
    z = -5:1:5;
    f = (1/sqrt(2*pi))*exp(-z.^2/2);
    plot(z,f);
    xlabel('z');
    ylabel('frequency');
    3*. The trajectory of an object can be modeled as

    𝑔 2
    𝑦 = (𝑡𝑎𝑛𝜃0 )𝑥 − 𝑥 + 𝑦0
    2𝑣02 𝑐𝑜𝑠 2 𝜃0

    where y = height (m), θ0 = initial angle (radians), x = horizontal distance (m), g =


    gravitational acceleration (9.81 m/s2), v0 = initial velocity (m/s), and y0 = initial height.
    Use MATLAB to find the trajectories for y0 = 0 and v0 = 28 m/s for initial angles ranging
    from 15 to 75o in increments of 15o. Employ a range of horizontal distances from x = 0 to
    80 m in increments of 5 m. The results should be assembled in an array where the first
    dimension (rows) corresponds to the distances, and the second dimension (columns)
    corresponds to the different initial angles. Use this matrix to generate a single plot of the
    heights versus horizontal distances for each of the initial angles. Employ a legend to
    distinguish among the different cases, and scale the plot so that the minimum height is
    zero using the axis command.

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