A pendulum is a rod hanging vertically from its top end that swings from side to side due
to the force of gravity. The only thing that affects speed of pendulum swinging is its
length and the strength of gravity. A pendulum works by converting energy back and
forth between potential and kinetic.

#### Algorithm:

##### Input to the algorithm:

Coordinates for clock and pendulum circle, segments, radius and vertex for line segment.
##### Output of the algorithm:

Displaying the clock with pendulum.
##### Data Variables:

x1, y1 : coordinates for clock circle.
x2, y2 : coordinates for pendulum circle.
segments: stores the number of segments required for drawing a circle.
theta: stores the angle of circle.
##### Algorithm for clock with pendulum:

1. Start
2. angle=135, inc=1, segments=25, x1=0,y1=0;
3. Calculate theta = 2.0f * 3.14 * (ii / segments);
4. Calculate x and y component:
5. angle>225 and angle<135 for movement of line and circle.
6. Draw Circles(x1,y1,angle) of watch
7. Draw line and circle (segments, radius = 2, x1,y1) of pendulum
8. Stop.

#### Program:

```#include <math.h>
#include <GL/glut.h>

using namespace std;

float angle = 135;
float inc = 1.0;

void drawCircle(float segments, float radius, float sx, float sy)
{
glBegin(GL_LINE_LOOP);
for(int ii = 0; ii < segments; ii++)
{
float theta = 2.0f * 3.1415926f * float(ii) / float(segments);//get the current angle

float x = radius * cosf(theta);//calculate the x component
float y = radius * sinf(theta);//calculate the y component

glVertex2f(x + sx, y + sy);// vertex of circles

}
glEnd();
}

void drawCircles(float x1,float y1,float angle) {
float segments = 25;
// Draw the original circle
glLineWidth(4);
glColor3f(0,1,1);

glColor3f(1,0,1);
glLineWidth(3);
glBegin(GL_LINES);  //hour line
glVertex2f(x1,y1);
glVertex2f(1,1);
glEnd();

glColor3f(1,1,0);
glLineWidth(1); //time line
glBegin(GL_LINES);
glVertex2f(x1,y1);
glVertex2f(x1,2);
glEnd();

// Draw the pendulum circle
float y2 = 10 * cos(radian);
float x2 = 10 * sin(radian);

glColor3f(1,1,1);

glBegin(GL_LINES);    // vertex of lines
glVertex2f(x1,-2.8);
glVertex2f(x2,y2);
glEnd();

}

void display(void) {
glClearColor (0.0,0.0,0.0,1.0);
glClear (GL_COLOR_BUFFER_BIT);
glTranslatef(-10,0,-30);
glColor3f(1,1,1);

if (angle>225) {
angle = 225;
inc = -inc;
}
if (angle<135) {
angle = 135;
inc = -inc;
}
angle += inc;
drawCircles(0,0,angle);
glutSwapBuffers();

}

void reshape (int w, int h) {
glMatrixMode (GL_PROJECTION);  //maps camera to screen
gluPerspective (100, (GLfloat)w / (GLfloat)h, 0.5, 100.0);
glMatrixMode (GL_MODELVIEW);   // maps objects to local coordinates
}

int main (int argc, char **argv) {
glutInit (&argc, argv);
glutInitWindowSize (800, 600);
glutInitWindowPosition (0, 0);
glutCreateWindow ("A Pendulum");

glutDisplayFunc (display);
glutIdleFunc (display);
glutReshapeFunc (reshape);
glutMainLoop ();
return 0;
}```

#### Output:

1. Do you know if it's possible to make the clock move according to the pendulum movement?

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