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

[Flaneuse]

The following is the Rayleigh Plesset equation, modified so as to be specific to the phenomenon of sonoluminescence.

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

 

[omkar13]

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?

 

[Mute]

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.

 

[Flaneuse]

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!

 

[CellCoree]

To graph this equation, you can use any graphing software or online program that allows you to plot functions. Excel, for example, has a function plotting feature that you can use.

To start, you will need to define the constants in the equation, such as ρ, p_g, P_0, η, and γ. These values can be obtained from the literature or from your own experiments.

Next, you will need to plot the function for R(t) using the Rayleigh Plesset equation. This can be done by entering the equation into the function plotter and setting the time variable, t, as the independent variable. The resulting graph will show the behavior of R over time.

To compare this graph with another one, you can either plot both functions on the same graph or plot them separately and then compare them side by side. This will allow you to see the differences in the maxima and minima of R between the two graphs.

When plotting the function for R(t), you can also vary the value of P(t) to see how it affects the graph. This will give you a better understanding of how the pressure changes affect the behavior of R.

Overall, using a graphing software or online program will allow you to easily visualize the behavior of R in the Rayleigh Plesset equation and compare it with other graphs. This can help you gain a better understanding of the phenomenon of sonoluminescence and how different variables affect it.