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Final

#include <gd.h>
#include <stdio.h>
#include <math.h>
 
#define WIDTH 800
#define HEIGHT 600
#define SCALE 100
 
//繪製電阻形狀
void drawResistor(gdImagePtr im, int x1, int y, int width, int height) {
    int startX = x1 ;
    int endX = x1 + width ;
 
    // 第一段直線向前走一段
    gdImageLine(im, startX, y, startX + width / 4 , y, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向上45度
    gdImageLine(im, startX + width / 4 , y, startX + width / 4 + height / 2 , y - height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向下90度
    gdImageLine(im, startX + width / 4 + height / 2, y - height / 2 , startX + width / 4 + height / 2 + height , y + height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向上90度
    gdImageLine(im, startX + width / 4 + height / 2 + height, y + height / 2, startX + width / 4 + height / 2 + 2 * height, y - height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向下90度
    gdImageLine(im, startX + width / 4 + height / 2 + 2 * height , y - height / 2, startX + width / 4 + height / 2 + 3 * height , y + height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向上90度
    gdImageLine(im, startX + width / 4 + height / 2 + 3 * height, y + height / 2 , startX + width / 4 + height / 2 + 4 * height, y - height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向下90度
    gdImageLine(im, startX + width / 4 + height / 2 + 4 * height, y - height / 2, startX + width / 4 + height / 2 + 5 * height, y + height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
  // 向上45度
    gdImageLine(im, startX + width / 4 + height / 2 + 5 * height, y + height / 2, startX + width / 4 + height / 2 + 5 * height + height / 2, y, gdImageColorAllocate(im, 0, 0, 255));
 
  gdImageLine(im, startX + width / 4 + height / 2 + 5 * height + height / 2, y, startX + width / 4 + height / 2 + 5 * height + height / 2 +5 , y, gdImageColorAllocate(im, 0, 0, 255));
 
 
  {
    int startX = 100;
  gdImageColorAllocate(im, 0, 0, 255);
 
 
    // 第一段直線向前走一段
    gdImageLine(im, startX, y, startX + width / 4 , y, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向上45度
    gdImageLine(im, startX + width / 4 , y, startX + width / 4 + height / 2 , y - height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向下90度
    gdImageLine(im, startX + width / 4 + height / 2, y - height / 2 , startX + width / 4 + height / 2 + height , y + height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向上90度
    gdImageLine(im, startX + width / 4 + height / 2 + height, y + height / 2, startX + width / 4 + height / 2 + 2 * height, y - height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向下90度
    gdImageLine(im, startX + width / 4 + height / 2 + 2 * height , y - height / 2, startX + width / 4 + height / 2 + 3 * height , y + height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向上45度
      gdImageLine(im, startX + width / 4 + height / 2 + 3 * height, y + height / 2, startX + width / 4 + height / 2 + 3 * height + height / 2, y, gdImageColorAllocate(im, 0, 0, 255));
 
    gdImageLine(im, startX + width / 4 + height / 2 + 3 * height + height / 2, y, startX + width / 4 + height / 2 + 3 * height + height / 2 +5 , y, gdImageColorAllocate(im, 0, 0, 255));
 }
 
  {
    int startX = 585;
  gdImageColorAllocate(im, 0, 0, 255);
 
 
    // 第一段直線向前走一段
    gdImageLine(im, startX, y, startX + width / 4 , y, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向上45度
    gdImageLine(im, startX + width / 4 , y, startX + width / 4 + height / 2 , y - height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向下90度
    gdImageLine(im, startX + width / 4 + height / 2, y - height / 2 , startX + width / 4 + height / 2 + height , y + height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向上90度
    gdImageLine(im, startX + width / 4 + height / 2 + height, y + height / 2, startX + width / 4 + height / 2 + 2 * height, y - height / 2, gdImageColorAllocate(im, 0, 0, 255));
    // 向下90度
    gdImageLine(im, startX + width / 4 + height / 2 + 2 * height , y - height / 2, startX + width / 4 + height / 2 + 3 * height , y + height / 2, gdImageColorAllocate(im, 0, 0, 255));
 
    // 向上45度
      gdImageLine(im, startX + width / 4 + height / 2 + 3 * height, y + height / 2, startX + width / 4 + height / 2 + 3 * height + height / 2, y, gdImageColorAllocate(im, 0, 0, 255));
 
    gdImageLine(im, startX + width / 4 + height / 2 + 3 * height + height / 2, y, startX + width / 4 + height / 2 + 3 * height + height / 2 +5 , y, gdImageColorAllocate(im, 0, 0, 255));
 
    gdImageLine(im, 100, y +20, 700, y +20, gdImageColorAllocate(im, 0, 255, 0));
 
}
}
 
int main() {
    gdImagePtr im;
    FILE *outputFile;
 
    // 創建圖像物件
    im = gdImageCreateTrueColor(WIDTH, HEIGHT);
    if (im == NULL) {
        fprintf(stderr, "Error creating GD image.\n");
        return 1;
    }
 
    outputFile = fopen("1.png", "wb");
    if (outputFile == NULL) {
        fprintf(stderr, "Error opening the output file.\n");
        return 1;
    }
 
    //配置顏色
    int black, white, red, blue, green;
 
    black = gdImageColorAllocate(im, 0, 0, 0);
    white = gdImageColorAllocate(im, 255, 255, 255);
    red = gdImageColorAllocate(im, 255, 0, 0);
    blue = gdImageColorAllocate(im, 0, 0, 255);
green = gdImageColorAllocate(im, 0, 255, 0);
    gdImageFilledRectangle(im, 0, 0, WIDTH - 1, HEIGHT - 1, white);
 
    // 繪製牆面
    gdImageLine(im, SCALE, SCALE, SCALE, HEIGHT - SCALE, black);
    gdImageLine(im, WIDTH - SCALE, SCALE, WIDTH - SCALE, HEIGHT - SCALE, black);
 
   // 繪製彈簧(電阻)
    drawResistor(im, WIDTH / 3 + SCALE / 2, HEIGHT / 2, SCALE / 2, SCALE / 4);
 
    // 繪製質量（方形）
    gdImageFilledRectangle(im, WIDTH / 3 - SCALE / 2, HEIGHT / 2 - SCALE / 2, WIDTH / 3 + SCALE / 2, HEIGHT / 2 + SCALE / 2, red);
    gdImageFilledRectangle(im, WIDTH * 2 / 3 - SCALE / 2, HEIGHT / 2 - SCALE / 2, WIDTH * 2 / 3 + SCALE / 2, HEIGHT / 2 + SCALE / 2, red);
 
  gdImageFilledRectangle(im, 100, HEIGHT +300, 700, HEIGHT /2 +49 , black);
 
 
    //生成圖片
    gdImagePng(im, outputFile);
    fclose(outputFile);
    gdImageDestroy(im);
 
    return 0;
}

#include <stdio.h>
#include <math.h>
 
#define TIME_STEP 0.01 // 時間步長
#define SIMULATION_TIME 10.0 // 模擬時間
 
// 物體參數
#define m1 2.0
#define m2 3.0
#define k1 0.5
#define k2 1.0
#define k3 1.5
#define c1 0.25
#define c2 0.33
#define c3 0.5
#define X1_initial 1.0
#define X2_initial -0.5
#define V0 0.0
 
// 計算阻尼力
double dampingForce(double c, double v) {
    return -c * v;
}
 
// 模擬物體運動
void simulateMotion() {
  double X1 = X1_initial;
  double X2 = X2_initial;
  double V1 = V0;
  double V2 = V0;
 
  FILE *fp;
  fp = fopen("motion_data.txt", "w");
 
  for (double t = 0; t <= SIMULATION_TIME; t += TIME_STEP) {
  double F1 = -k1 * (X1 - 0) - c1 * (V1 - 0); // 第一個物體受到的合力
  double F2 = -k2 * (X2 - X1) - c2 * (V2 - V1); // 第二個物體受到的合力
  double F3 = -k3 * (X2 - 0) - c3 * (V2 - 0); // 第二個物體受到的合力
 
  double a1 = F1 / m1; // 第一個物體的加速度
  double a2 = F2 / m2; // 第二個物體的加速度
 
// 更新速度和位置
   V1 += a1 * TIME_STEP;
   V2 += a2 * TIME_STEP;
 
  X1 += V1 * TIME_STEP;
  X2 += V2 * TIME_STEP;
 
// 在文件寫入時紀錄 m1 和 m2 的位置和速度數據
  fprintf(fp, "%lf %lf %lf %lf %lf\n", t, X1, X2, V1, V2);
    }
 
 
  fclose(fp);
}
 
int main() {
    simulateMotion();
    return 0;
}

#include <stdio.h>
 
int main() {
    FILE *gnuplotPipe = popen("gnuplot", "w");
    if (gnuplotPipe) {
        fprintf(gnuplotPipe, "set terminal png\n");
        fprintf(gnuplotPipe, "set output 'motion_plot.png'\n");
        fprintf(gnuplotPipe, "set xlabel 'Time'\n");
        fprintf(gnuplotPipe, "set ylabel 'Position / Velocity'\n");
        fprintf(gnuplotPipe, "plot 'motion_data.txt' using 1:2 with lines title 'm1 position', 'motion_data.txt' using 1:3 with lines title 'm2 position', 'motion_data.txt' using 1:4 with lines title 'm1 velocity', 'motion_data.txt' using 1:5 with lines title 'm2 velocity'\n");
        fprintf(gnuplotPipe, "exit\n");
        fflush(gnuplotPipe);
        pclose(gnuplotPipe);
    } else {
        printf("Error opening pipe to Gnuplot.\n");
    }
    return 0;
}

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