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Here is the code I have been trying to solve:

\[Xi] = 0.1; R1 = 50*10^-9; \[Rho]ag = 10.49*10^3;
cd=0.5*10^-8
f2=-cd*xs'[t];
f3=(4/3)*\[Pi]*\[Xi]*(R1)^3*\[Rho]ag*xs''[t];
ftotal=f2-f3;
AA=NDSolve[{ftotal == 0, xs[2700] == 300 10^-9 , xs''[2700] == 0}, xs, {t, 0, 3031}];
Plot[xs /. AA, {t, 0, 3031}]

First of all, I have chosen the boundary conditions from the graph I am trying to reproduce and I am not sure they are true or not. I have attached the original graph. this is the original graph

Secondly my problem is that the graph I plot in Mathematica is empty!! I have attached a screenshot.

this is the screenshot of my code

Does anyone have any idea how can I plot this graph?

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    $\begingroup$ what do you see after you issue the command NDSolve but before you do the plot? Do you get an errors from NDSolve? Does it give a solution? $\endgroup$
    – Nasser
    Aug 25 '21 at 8:00
  • $\begingroup$ No I do not receive any errors and yes it generates a solution with this format: {{xs -> InterpolatingFunction[{{0., 3031.}}, $\endgroup$ Aug 25 '21 at 8:19
  • $\begingroup$ Try cd=0.5*10^-8;ξ=1;ρag=1;R1=1;f2=-cd*xs'[t]; f3=(4/3)*Pi*ξ*(R1)^3*ρag*xs''[t]; ftotal=f2-f3; AA=NDSolve[{ftotal==0,xs[2700]==300*10^-9,xs''[2700]==0},xs,{t,0,3031}][[1]]; Table[xs[t]/.AA,{t, 0,3031,30}] and adjust values for ξ,ρag,R1 and step size in the Table until you begin to see reasonable (Real) values. Then you can try Plot $\endgroup$
    – Bill
    Aug 25 '21 at 8:23

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