Mass-Spring System
Description
This MATLAB GUI simulates the solution to the ordinary differential equation m y'' + c y' + k y = F(t), describing the response of a one-dimensional mass spring system with forcing function F(t) given by (i) a unit square wave or (ii) a Dirac delta function (e.g. "hammerblow"). Without loss of generality, m is set to 1.
The GUI allows the user (i) to choose the damping coefficient c/m and square natural frequency k/m of the system; (ii) to change the height N (and, consequently, the width 1/N) of the unit forcing function, or to choose the forcing function to be an "infinitely tall" unit forcing function, i.e. a Dirac delta function; (iii) to zoom in on the immediate response of the system, in order to compare the case where the forcing function is given by a large but finite unit square wave (e.g. with N = 20) with the case where the forcing function is given by the Dirac delta function.
In each case, the program graphs the forcing function and the solution of the spring-mass system on the same axes.
How to use the GUI
Use the sliders to change the values of the parameters c/m, k/m, or N.
Click on the button labeled Infinite to change the forcing to a delta function. Click on Finite to come back to a square wave forcing.
Click on Close up centered at (x,y) = (1,0) to zoom in near the origin.
Download
To download the GUI, right click on each of the links below, and save the corresponding files into a directory. Set the MATLAB path to that directory and then type Mass_Spring_System at the MATLAB prompt.
Type help Mass_Spring_System at the MATLAB prompt if you need to be reminded of how to use the GUI.
GUI developed by Benjamin Dyhr, Spring 2007.