Hello, I am new at this and have some problems solving a differential equation in Mathematica.
I want to solve this equation: Felectrical+Fsurfaceviscosity=ma
In which F_electrical is obtained from a partial derivative relative to xs. I have written my code bellow:
\[Epsilon]0 = 8.85*10^-12 ; \[Epsilon]g =
42*\[Epsilon]0; \[Xi] = 0.1; R1 = 50*10^-9;
\[Rho]ag = 10.49*10^3; cd = 0.5 10^-8;
\[Epsilon]rel = ((\[Epsilon]g - \[Epsilon]0)/(\[Epsilon]g + \
\[Epsilon]0));
x1 = 500 10^-9; z1 = 5 10^-9; z1s = -5 10^-9; zs =
5 10^-9; x2 = -500 10^-9; z2 = 5 10^-9; z2s = -5 10^-9;
U[xs_]:=(1/(Sqrt[(xs - x1)^2 + (zs - z1)^2])^3 - (
3* (xs - x1)^2)/(Sqrt[(xs - x1)^2 + (zs - z1)^2])^5 +
1/(Sqrt[(xs - x2)^2 + (zs - z2)^2])^3 - (
3* (xs - x2)^2)/(Sqrt[(xs - x2)^2 + (zs - z2)^2])^5)-\[Epsilon]rel*(1/(Sqrt[(xs - x1)^2 + (zs - z1s)^2])^3 - (
3* (xs - x1)^2)/(Sqrt[(xs - x1)^2 + (zs - z1s)^2])^5 +
1/(Sqrt[(xs - x2)^2 + (zs - z2s)^2])^3 - (
3* (xs - x2)^2)/(Sqrt[(xs - x2)^2 + (zs - z2s)^2])^5+1/(Sqrt[(zs - zss)^2])^3);
F_electrical=-U'[xs];
F_surfaceviscositi = -cd*xs'[t];
ma=4/3*\[Pi]*\[Xi]*(R1)^3*\[Rho]ag*xs''[t];
F_total=F_electrical+F_surfaceviscosity-ma;
NDSolve[{ftotal == 0, xs[0] == 100 10^-9 ,
xs[2700] == 300 10^-9}, xs, {t, 0, 3031}] ;
When I try to plot this, I get tones of errors! I should mention that no boundary conditions are specified in the reference article and I have chosen them from the original graph itself which I have attached a picture of it.
Does anyone have any idea how I can plot my graph?