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#include <stdio.h>
#include <gd.h>

// Function to draw the mass-spring-damper system
void draw_system(const char* filename) {
    int width = 600;
    int height = 300;
    int x_margin = 50;
    int y_margin = 50;
    int mass_radius = 20;
    int spring_width = 4;
    int damper_width = 4;

    gdImagePtr img = gdImageCreate(width, height);
    int background_color = gdImageColorAllocate(img, 255, 255, 255);
    int mass_color = gdImageColorAllocate(img, 0, 0, 0);
    int spring_color = gdImageColorAllocate(img, 0, 0, 0);
    int damper_color = gdImageColorAllocate(img, 0, 0, 0);
    int wall_color = gdImageColorAllocate(img, 0, 0, 0);

    // Draw left wall
    gdImageLine(img, x_margin, y_margin, x_margin, height - y_margin, wall_color);

    // Draw mass 1
    int x1 = x_margin + 2 * mass_radius;
    int y1 = height / 2;
    gdImageFilledEllipse(img, x1, y1, mass_radius, mass_radius, mass_color);

    // Draw spring 1
    int spring1_start_x = x_margin;
    int spring1_end_x = x1 - mass_radius;
    int spring1_y = y1;
    gdImageLine(img, spring1_start_x, spring1_y, spring1_end_x, spring1_y, spring_color);
    gdImageSetThickness(img, spring_width);
    gdImageLine(img, spring1_start_x, spring1_y, spring1_end_x, spring1_y, spring_color);
    gdImageSetThickness(img, 1);

    // Draw damper 1
    int damper1_start_x = x_margin / 2;
    int damper1_end_x = x1 - mass_radius;
    int damper1_y = y1;
    gdImageLine(img, damper1_start_x, damper1_y, damper1_end_x, damper1_y, damper_color);
    gdImageSetThickness(img, damper_width);
    gdImageLine(img, damper1_start_x, damper1_y, damper1_end_x, damper1_y, damper_color);
    gdImageSetThickness(img, 1);

    // Draw mass 2
    int x2 = width - x_margin - 2 * mass_radius;
    int y2 = height / 2;
    gdImageFilledEllipse(img, x2, y2, mass_radius, mass_radius, mass_color);

    // Draw spring 2
    int spring2_start_x = x2 + mass_radius;
    int spring2_end_x = width - x_margin;
    int spring2_y = y2;
    gdImageLine(img, spring2_start_x, spring2_y, spring2_end_x, spring2_y, spring_color);
    gdImageSetThickness(img, spring_width);
    gdImageLine(img, spring2_start_x, spring2_y, spring2_end_x, spring2_y, spring_color);
    gdImageSetThickness(img, 1);

    // Draw damper 2
    int damper2_start_x = width - x_margin + mass_radius;
    int damper2_end_x = x2 + mass_radius;
    int damper2_y = y2;
    gdImageLine(img, damper2_start_x, damper2_y, damper2_end_x, damper2_y, damper_color);
    gdImageSetThickness(img, damper_width);
    gdImageLine(img, damper2_start_x, damper2_y, damper2_end_x, damper2_y, damper_color);
    gdImageSetThickness(img, 1);

    // Draw right wall
    gdImageLine(img, width - x_margin, y_margin, width - x_margin, height - y_margin, wall_color);

    // Save the image to a file
    FILE *output_file = fopen(filename, "wb");
    gdImagePng(img, output_file);
    fclose(output_file);

    // Free the memory used by the image
    gdImageDestroy(img);
}

int main() {
    draw_system("mass_spring_damper_system.png");
    return 0;
}

第二題

#include <stdio.h>

// System parameters
#define M1 2.0
#define M2 3.0
#define K1 0.5
#define K2 1.0
#define K3 15.0
#define C1 0.25
#define C2 0.33
#define C3 0.5

// Function to calculate the derivative of the state
void calculate_derivative(double t, double state[4], double derivative[4]) {
    derivative[0] = state[2];  // dx1/dt = v1
    derivative[1] = state[3];  // dx2/dt = v2

    double delta_x = state[0] - state[1];

    // dv1/dt
    derivative[2] = -(K1 * state[0] + K2 * delta_x) / M1;

    // dv2/dt
    derivative[3] = -(K3 * state[1] - K2 * delta_x) / M2;
}

// Euler's Method for solving the system
void euler_method(double t_initial, double t_final, double dt, double initial_conditions[4]) {
    FILE *output_file;
    output_file = fopen("trajectory_data.txt", "w");

    double t = t_initial;
    double state[4];
    for (int i = 0; i < 4; ++i) {
        state[i] = initial_conditions[i];
    }

    while (t <= t_final) {
        fprintf(output_file, "%f %f %f %f %f\n", t, state[0], state[1], state[2], state[3]);

        double derivative[4];
        calculate_derivative(t, state, derivative);

        for (int i = 0; i < 4; ++i) {
            state[i] += derivative[i] * dt;
        }

        t += dt;
    }

    fclose(output_file);
}

int main() {
    // Define the initial conditions
    double initial_conditions[4] = {1.0, -0.5, 0.0, 0.0};  // x1, x2, v1, v2

    // Time parameters
    double t_initial = 0.0;
    double t_final = 10.0;
    double dt = 0.01;

    // Solve the system using Euler's Method
    euler_method(t_initial, t_final, dt, initial_conditions);

    return 0;
}

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