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Spring-Mass System - Panel
Spring-Mass System - Panel

 

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If you have never used MATLAB before, we recommend watching some of these videos from The MathWorks , in particular the Getting Started video. . You can go through the videos either before or after completing this tutorial.

Spring-Mass Harmonic Oscillator in MATLAB

Created using MATLAB R2013a

Problem Specification

Consider a spring-mass system shown in the figure below.



Image Added

Applying F = ma in the x-direction, we get the following differential equation for the location x(t) of the center of the mass:

Latex
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h1. Spring-Mass Harmonic Oscillator in MATLAB

Consider a spring-mass system shown in the figure below.

\\
\\ [!spring_mass.png|width=350!|^spring_mass.png]\\
\\

Applying _F = ma_ in the x-direction, we get the following differential equation for the location x(t) of the center of the mass:
{latex} 
\[
m \ddot{x} + k x =0
\]
{latex}

The

...

initial

...

conditions

...

at

...

t=0

...

are

Latex
 
{latex} 
\[
x(0)=1,
\]

and

Latex
{latex} 
and 
{latex} 
\[
v(0)=\dot{x} ̇(0)=0
\]
{latex} 

The first condition above specifies the initial location _

The first condition above specifies the initial location x(0)

...

and

...

the

...

second

...

condition,

...

the

...

initial

...

velocity

...

v(0)

...

.


We’ll solve this differential equation numerically, i.e.

...

integrate

...

it

...

in

...

time

...

starting

...

from

...

the

...

initial

...

conditions

...

at

...

t=0,

...

using

...

MATLAB.

...

We’ll use

...

Euler's

...

method

...

to

...

perform

...

the

...

numerical

...

integration. Some other topics covered in this tutorial are:

  • Making a plot of mass position vs. time and comparing it to the analytical solution
  • Separating out the Euler's method in a MATLAB "function"
  • Collecting multiple parameters in one box using "structures"

In the process, you'll be exposed to the following handy MATLAB utilities:

  • Debugger to understand and step through code
  • Code analyzer to check code
  • Profiler to time code


Go to Step 1: Euler Integration

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