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/**********************************************************************
* File: vibration.cpp
* Display the positions of damped free vibrations of
* overdamped, critical damped, underdamped systems.
* 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>
#include <chplot.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 t0, tf;
int num = 100; // number of points for plotting
CPlot plot;
t0 = 0;
tf = 10;
plot.title("Damped Free Vibration");
plot.label(PLOT_AXIS_X, "time (second)");
plot.label(PLOT_AXIS_Y, "x");
plot.func2D(t0, tf, num, overdamped);
plot.legend("overdamped", 0);
plot.func2D(t0, tf, num, criticaldamped);
plot.legend("critically damped", 1);
plot.func2D(t0, tf, num, underdamped);
plot.legend("underdamped", 2);
/* create png file for display on the web */
plot.outputType(PLOT_OUTPUTTYPE_FILE, "png", "vibration.png");
plot.plotting();
return 0;
}
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