## Mathematics & Science
Learning Center |
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## Applications of Differential Equations## A Suspended Wire
This time the result is a little more obscure: NDSolve[{y''[x]==(0.5/40)*Sqrt[1+(y'[x])^2], y[0]==0,
y'[0]==0}, y[x], {x,-5,5}] The result is in the form of an InterpolatingFunction, which is
something we've seen before, specifically in the numerical solvers laboratory.
From experience, we know that though it may look a little strange, it is
possible to use this solution for most of the usual purposes, i.e. we can
substitutes values into it, and we can plot its graph. Recall that the
{-5., 5.} specified in the solution tells us the domain upon which it
may be used. (The solution is invalid outside of -5 ≤ We were asked to plot a graph of the wire in the instructions to the
original problem, so we'd better get on with the job. Before we can use the
function properly it needs to be retrieved from within the replacement rule
that wire1=%[[1,1,2]] which says to get the previous result (the percent sign, %, means previous result, remember?), and take its first row, first column, second part, and read the result into a new variable called wire1. Go back to Welcome back. Let's move on to making the graph... |
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ODE Laboratories: A Sabbatical Project by Christopher A. Barker©2017 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA e-mail: cbarker@deltacollege.edu |