/**********************************************************************
* File: vibration.c
* Animate the damped free vibration of
* overdamped, critical damped, underdamped systems.
* The output is for animation coordinate data.
* (1) Run this program in Ch as follows:
*      vibration.c | qanimate
*                or
*      vibration.c > tmp1.qnm
*      qanimate tmp1.qnm
* (2) Click "Go" to view the animation
* See CHHOME/docs/qanimate.pdf for detailed description of this program.
* Note: The details about this damped free vibration can be found in
* an exercise in Chapter 6 Functions in the book 
* "C for Engineers and Scientists: An Interpretive Approach"
* by Harry H. Cheng, published by McGraw-Hill, 2009,
* ISBN: 0073376051, ISBN-13: 978-0073376059.
**********************************************************************/
#include <stdio.h>
#include <math.h>

/* The amplitude of the vibration is 4.
   The initial velocity of the vibration is 0 */
double overdamped(double t) {
    return 4.12*exp(-1.57*t) - 0.12*exp(-54.2*t);
}

double criticaldamped(double t) {
    return 4*(1+6*t)*exp(-6*t);
}

double underdamped(double t) {
    return 4.06*exp(-0.5*t)*sin(3*t+1.4);
}

int main() {
    double t, t0, tf;          // time
    double y1, y2, y3;         //displacement
    double pin1x = 0, pin1y=7, // pin 1 
           pin2x = 4, pin2y=7, // pin 2
           pin3x = 8, pin3y=7; // pin 3

    /* A comment line starting with # */
    printf("# qanimate data for animation of vibration systems\n");
    /* The title displayed on the animation */
    printf("title \"Damped Free Vibration\"\n");
    printf("fixture\n");
    /* The primitives following fixture */
    printf("groundpin %f %f angle 180 joint %f %f\n", pin1x, pin1y, pin1x, pin1y);
    printf("line %f %f %f %f\n", pin1x, pin1y, pin1x, pin1y-1 );
    printf("text %f %f \"overdamped\"\n", pin1x+0.5, pin1y);
    printf("groundpin %f %f angle 180 joint %f %f\n", pin2x, pin2y, pin2x, pin2y);
    printf("line %f %f %f %f\n", pin2x, pin2y, pin2x, pin2y-1 );
    printf("text %f %f \"critical damped\"\n", pin2x+0.5, pin2y);
    printf("groundpin %f %f angle 180 joint %f %f\n", pin3x, pin3y, pin3x, pin3y);
    printf("line %f %f %f %f\n", pin3x, pin3y, pin3x, pin3y-1 );
    printf("text %f %f \"underdamped\"\n", pin3x+0.5, pin3y);
    printf("dot 11 7 pen white\n"); // to display all text corretly
    printf("animate restart\n");

    t0 = 0;
    tf = 10;
    for(t = t0; t<tf; t += 0.01) {
        y1 = overdamped(t);
        y2 = criticaldamped(t);
        y3 = underdamped(t);
        printf("rectangle %f %f %f %f fill red \\\n",-0.5, y1-1.0, 1.0, 1.0);
        printf("spring %f %f %f %f \\\n", pin1x, pin1y-1, pin1x, y1);
        printf("rectangle %f %f %f %f fill green \\\n", pin2x-0.5, y2-1.0, 1.0, 1.0);
        printf("spring %f %f %f %f \\\n", pin2x, pin2y-1, pin2x, y2);
        printf("rectangle %f %f %f %f fill blue \\\n", pin3x-0.5, y3-1.0, 1.0, 1.0);
        printf("spring %f %f %f %f \n", pin3x, pin3y-1, pin3x, y3);
    }
    return 0;
}