Forced Oscillations

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An Application of Fourier Series


Copyright 1996
Gary S. Stoudt
Mathematics Department
Indiana University of PA
Indiana, PA 15705
GSSTOUDT@grove.iup.edu

Adapted from Erwin Kreysig, "Advanced Engineering Mathematics", Wiley.

Here are the orthogonal functions.

In[1]:=

  Clear[u,v,L]

In[2]:=

  u[x_,L_,n_]:=Cos[n Pi x/L]

In[3]:=

  ColumnForm[Table[u[x,L,k],{k,0,10}]]

Out[3]=

  1
      Pi x
  Cos[----]
       L
      2 Pi x
  Cos[------]
        L
      3 Pi x
  Cos[------]
        L
      4 Pi x
  Cos[------]
        L
      5 Pi x
  Cos[------]
        L
      6 Pi x
  Cos[------]
        L
      7 Pi x
  Cos[------]
        L
      8 Pi x
  Cos[------]
        L
      9 Pi x
  Cos[------]
        L
      10 Pi x
  Cos[-------]
         L

Note that u[x,L,0]=1 and this will be used.

In[4]:=

  v[x_,L_,n_]:=Sin[n Pi x/L]

In[5]:=

  ColumnForm[Table[v[x,L,k],{k,0,10}]]

Out[5]=

  0
      Pi x
  Sin[----]
       L
      2 Pi x
  Sin[------]
        L
      3 Pi x
  Sin[------]
        L
      4 Pi x
  Sin[------]
        L
      5 Pi x
  Sin[------]
        L
      6 Pi x
  Sin[------]
        L
      7 Pi x
  Sin[------]
        L
      8 Pi x
  Sin[------]
        L
      9 Pi x
  Sin[------]
        L
      10 Pi x
  Sin[-------]
         L

Note that v[x,L,0]=0 and will not be used.

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