How to define functions? (Variables are not been evaluated)

Questions
1

Hello, I am fairly new to using Mathematica and for some reason when I use one of the codes of line in the attachment, all of the variables won’t compute. For example if you run the code in the attachment the Fss5 nor Fss10 line of code won’t completely simplify out. Does anyone have any insight into this?

Thanks in advance!!

2

To define a function of a parameter, you need to add an underscore to the parameter, to make it a pattern:

\[Omega] = 8.0001*Pi;
\[CapitalOmega] = 2*Pi/To;
Subscript[r, n_] = n*\[CapitalOmega]/\[Omega];
\[Xi] = 0.05;
\[Rho]st = .1;
k = Fo/\[Rho]st;
Subscript[DAF, n_] = 
  1/Sqrt[((1 - Subscript[r, n]^2)^2 + (2 \[Xi]*Subscript[r, n])^2)];
Subscript[\[CapitalPsi], n_] = 
  ArcTan[(2 \[Xi]*Subscript[r, n])/(1 - Subscript[r, n]^2)];

The plot does not work because you have not given a numeric value to the symbol To. For example, the following computes fine:

To = 1;
\[Omega] = 8.0001*Pi;
\[CapitalOmega] = 2*Pi/To;
Subscript[r, n_] = n*\[CapitalOmega]/\[Omega];
\[Xi] = 0.05;
\[Rho]st = .1;
k = Fo/\[Rho]st;
Subscript[DAF, n_] = 
  1/Sqrt[((1 - Subscript[r, n]^2)^2 + (2 \[Xi]*Subscript[r, n])^2)];
Subscript[\[CapitalPsi], n_] = 
  ArcTan[(2 \[Xi]*Subscript[r, n])/(1 - Subscript[r, n]^2)];
Subscript[F, 
  ss1] = (Fo/(3 k)) + (Subscript[DAF, n]*(4.5 Fo/(k*(n*Pi)^2))*
      Cos[(n*\[CapitalOmega]*t) - Subscript[\[CapitalPsi], n]]) /. 
   n -> 1;
Subscript[F, 
  ss5] = (Fo/(3 k)) + 
   Sum[(Subscript[DAF, n]*(4.5 Fo/(k*(n*Pi)^2))*
      Cos[(n*\[CapitalOmega]*t) - Subscript[\[CapitalPsi], n]]), {n, 
     1, 5, 1}];
Subscript[F, 
  ss10] = (Fo/(3 k)) + 
   Sum[(Subscript[DAF, n]*(4.5 Fo/(k*(n*Pi)^2))*
      Cos[(n*\[CapitalOmega]*t) - Subscript[\[CapitalPsi], n]]), {n, 
     1, 10, 1}];
Subscript[F, 
  sst] = {Subscript[F, ss1], Subscript[F, ss5], Subscript[F, ss10]};
Plot[Evaluate[Subscript[F, sst]], {t, 0, 2}, 
 AxesLabel -> {"Time(s)", "Displacement(in)"}]
3

Thank you so much for the Underscore Hint. It fixes everything!

4

@Gianluca Gorni

So if I want to compute the Fss10 variable for five different values of w being w=5,10,20,30,40(all times pi) and plot them on the same graph, how would I go about doing that? For some reason when I try to change the w value, it will not change accordingly. I can show you the code I am trying to use if you would like.

5

Here is a copy of the code..that is failing. It will only plot 1 line and it’s not even the right line.

6

To get a plot, you have to give a numerical value to k and [Xi]. On a different note, since your variables apparently depend on A, you may consider making it explicit, e.g.,

\[Omega][a_] = 5 a*Pi;
Subscript[r, a_, n_] = n*\[CapitalOmega]/\[Omega][a];
Subscript[DAF, a_, n_] = 
  1/Sqrt[((1 - Subscript[r, a, n]^2)^2 + (2 \[Xi]*Subscript[r, a, 
        n])^2)];
Subscript[\[CapitalPsi], a_, n_] = 
  ArcTan[(2 \[Xi]*Subscript[r, a, n])/(1 - Subscript[r, a, n]^2)];

That will save you all those code repetitions.