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Student Support Forum > General > > "Coefficient from matrix"

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Please answer this:2+5 =



Original Message (ID '126334') By Julius:
Ck[n_] := Table[ck[i], {i, n}] \[Phi]k[n_] := Table[Sin[(2 i - 1) \[Pi] x/L], {i, 1, n}] v[n_] := Ck[n].\[Phi]k[n] \[Theta][n_] := Ck[n].\[Phi]k[n] \[CapitalPi][n_] := 1/2 \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\(( \*SubscriptBox[\(EI\), \(z\)] \*SuperscriptBox[\(( \*SubscriptBox[\(\[PartialD]\), \(x, x\)]v[n])\), \(2\)] + \*SubscriptBox[\(GI\), \(T\)] \*SuperscriptBox[\(( \*SubscriptBox[\(\[PartialD]\), \(x\)]\[Theta][n])\), \(2\)] + \*SubscriptBox[\(EI\), \(\[Omega]\)] \*SuperscriptBox[\(( \*SubscriptBox[\(\[PartialD]\), \(x, x\)]\[Theta][ n])\), \(2\)])\) \[DifferentialD]x\)\) + 4 \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\(( \*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\(( \*FractionBox[\(x\), \(L\)] - \*FractionBox[ SuperscriptBox[\(x\), \(2\)], SuperscriptBox[\(L\), \(2\)]])\)*\((\[Theta][n] \(( \*SubscriptBox[\(\[PartialD]\), \(x, x\)]v[n])\) + \*SubscriptBox[\(\[Beta]\), \(z\)] \*SuperscriptBox[\(( \*SubscriptBox[\(\[PartialD]\), \(x\)]\[Theta][ n])\), \(2\)])\))\) \[DifferentialD]x\)\) + 1/2 \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\(( \*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\(( \*FractionBox[\(8\), SuperscriptBox[\(L\), \(2\)]])\) \*SubscriptBox[\(e\), \(z\)] \*SuperscriptBox[\((\[Theta][n])\), \(2\)])\) \[DifferentialD]x\)\) Subscript[k, bb][n_] := 1/2 \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\(( \*SubscriptBox[\(EI\), \(z\)] \*SuperscriptBox[\(( \*SubscriptBox[\(\[PartialD]\), \(x, x\)]v[ n])\), \(2\)])\) \[DifferentialD]x\)\) Subscript[k, cc][n_] := 1/2 \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\(( \*SubscriptBox[\(GI\), \(T\)] \*SuperscriptBox[\(( \*SubscriptBox[\(\[PartialD]\), \(x\)]\[Theta][n])\), \(2\)] + \*SubscriptBox[\(EI\), \(\[Omega]\)] \*SuperscriptBox[\(( \*SubscriptBox[\(\[PartialD]\), \(x, x\)]\[Theta][ n])\), \(2\)])\) \[DifferentialD]x\)\) + 4 \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\(( \*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\(( \*FractionBox[\(x\), \(L\)] - \*FractionBox[ SuperscriptBox[\(x\), \(2\)], SuperscriptBox[\(L\), \(2\)]])\)*\(( \*SubscriptBox[\(\[Beta]\), \(z\)] \*SuperscriptBox[\(( \*SubscriptBox[\(\[PartialD]\), \(x\)]\[Theta][ n])\), \(2\)])\))\) \[DifferentialD]x\)\) + 1/2 \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\(( \*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\(( \*FractionBox[\(8\), SuperscriptBox[\(L\), \(2\)]])\) \*SubscriptBox[\(e\), \(z\)] \*SuperscriptBox[\((\[Theta][n])\), \(2\)])\) \[DifferentialD]x\)\) Subscript[k, bc][n_] := 4 \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\(( \*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\(( \*FractionBox[\(x\), \(L\)] - \*FractionBox[ SuperscriptBox[\(x\), \(2\)], SuperscriptBox[\(L\), \(2\)]])\)*\((\[Theta][n] \(( \*SubscriptBox[\(\[PartialD]\), \(x, x\)]v[ n])\))\))\) \[DifferentialD]x\)\) k1[n_] := Sum[\!\( \*SubscriptBox[\(\[PartialD]\), \(ck[i]\)]\( \(\*SubscriptBox[\(k\), \(bb\)]\)[n]\)\), {i, n}] k3[n_] := Sum[\!\( \*SubscriptBox[\(\[PartialD]\), \(ck[i]\)]\( \(\*SubscriptBox[\(k\), \(cc\)]\)[n]\)\), {i, n}] k2[n_] := Sum[(\!\( \*SubscriptBox[\(\[PartialD]\), \(ck[i]\)]\( \(\*SubscriptBox[\(k\), \(bc\)]\)[n]\)\)), {i, n}] m[n_] := ( { {k1[n], k2[n]/2}, {k2[n]/2, k3[n]} } ) matrix[n_] := Table[Coefficient[m[n][[i]], ck[n]], {i, n}]