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h1. Spring-Mass Harmonic Oscillator in MATLAB

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

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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} 
\[
m \ddot{x} + k x =0
\]
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The initial conditions at _t=0_ are 
{latex} 
\[
x(0)=1,
\]
{latex} 
and 
{latex} 
\[
v(0)=\dot{x} ̇(0)=0
\]
{latex} 

The first condition above specifies the initial location _x(0)_ and the second condition, the initial velocity _v(0)_.   

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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
 
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[*Go to Step 1: Euler Integration*|SIMULATION:Spring-Mass System - Euler Integration]

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