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The first task here is to plug the constants into the equations, to see what were working with
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Here are the simple harmonic oscillator equations, and heres what I get if I plug in g = beta = 0; k = 2; and m = 0.5
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Heres the initial condition were starting from
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By the way, this transpose notation means Take a row vector and make it a column vector
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It can also mean Take a column vector and make it a row vector
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Now recall, forward Euler advances from the current state in the following fashion
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It takes the place where you are, computes the slope at that point, and walks along that slope for one timestep to get the next point, delta t later
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We have all this information except for the derivative vector
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To get the values for that vector, we need to plug this into this
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And if we do that that is, we evaluate the derivative [x, v] when x = -1 and v = -2 we get this value
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And then if we stuff that in here, we get the answer
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And if you do the addition right, youll see that this one is the correct answer