How can I graph this equation (Rayleigh Plesset for sonoluminescence)?

  • Thread starter Flaneuse
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  • #1
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The following is the Rayleigh Plesset equation, modified so as to be specific to the phenomenon of sonoluminescence.

R[itex]\ddot{R}[/itex] + 3/2([itex]\dot{R}[/itex]^2 = (1/ρ) (p[itex]_{g}[/itex] - P[itex]_{0}[/itex] -P(t) - 4η ([itex]\dot{R}[/itex]/R) - (2γ/R))

I'm trying to graph this for comparison of maxima and minima (of R) with another graph. If everything except R (and time derivatives of R) and P(t) are constants, how can I do this? (in Excel or an online program, for example; there is no need for actual solving of the problem if it can be graphed without doing so.)
 

Answers and Replies

  • #2
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Dude what is this P(t)? Is it any other equation or we have to make it as a subject like P(t)= something and plot it?
 
  • #3
Mute
Homework Helper
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To plot R vs. t you are going to have to solve the equation, at very least numerically. The simplest method for numerically solving equations is the Euler method, but it's also the least accurate and it probably doesn't work too well with non-linear differential equations. A decent numerical solution will probably be hard to calculate using Excel. The online website I know of that will solve DEs is www.wolframalpha.com. If you know all of your numbers and the function P(t), along with your initial conditions, then you might be able to get the site to plot it, though sometimes getting the site to interpret your input correctly can be tricky, so if you have access to Mathematica (which the program that wolframalpha runs off), then you can also use that to solve the equation numerically.
 
  • #4
23
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I tried Wolfram Alpha already, but it seemed to interpet what I was asking rather strangely; of course, it is quite possible that the way I typed it was less than perfect... I guess I'll have to either find a way to get Mathematica or solve it on my own. Thanks though!
 

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