Re: Equation problem
- To: mathgroup at smc.vnet.net
- Subject: [mg42213] Re: Equation problem
- From: bobhanlon at aol.com (Bob Hanlon)
- Date: Tue, 24 Jun 2003 01:26:59 -0400 (EDT)
- References: <bd6iuo$ca4$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Use FindRoot
Since n is not an integer, the upper limit of the summation should probably
include a Floor
r1=0.0298;
r2=0.0335;
n1=Floor[Abs[(r2-r1)/T]];
eqn1 = 2*Pi*Sum[r1+i*T,{i,0,n1}]==10
2*Pi*((1/2)*T*Floor[0.003700000000000002/Abs[T]]*
(Floor[0.003700000000000002/Abs[T]] + 1) +
0.0298*(Floor[0.003700000000000002/Abs[T]] + 1)) == 10
soln1 = FindRoot[eqn1, {T,{.00006,.0001}}]
FindRoot::frmp: Machine precision is insufficient to achieve the accuracy 1. x
10^-6
{T -> 0.00007400853629942335}
n1/.soln1
49
Plot[Evaluate[eqn1[[1]]-eqn1[[2]]],
{T,0.00007,.00008},
PlotStyle->RGBColor[1, 0, 0]];
Allowing the Sum to evaluate with a non-integer upper limit
n2=Abs[(r2-r1)/T];
eqn2 = 2*Pi*Sum[r1+i*T,{i,0,n2}]==10
2*Pi*(0.0298*(1 + 0.003700000000000002/Abs[T]) +
(0.001850000000000001*T*(1.*Abs[T] +
0.0037000000000000023))/Abs[T]^2) == 10
soln2 = FindRoot[eqn2, {T,{.00006,.0001}}]
{T -> 0.0000750721470872797}
n2/.soln2
49.28592219026773
Plot[Evaluate[eqn2[[1]]-eqn2[[2]]],
{T,0.00007,.00008},
PlotStyle->RGBColor[1, 0, 0]];
Bob Hanlon
In article <bd6iuo$ca4$1 at smc.vnet.net>, "Dan" <gentlemanjack at casino.com> wrote:
<< Subject: Equation problem
From: "Dan" <gentlemanjack at casino.com>
To: mathgroup at smc.vnet.net
Date: Mon, 23 Jun 2003 09:57:44 +0000 (UTC)
I need to solve the system of equations (in Mathematica notation):
r1 == 0.0298
r2 == 0.0335
n == Abs[(r2-r1)/T]
2*Pi*Sum[r1+i*T, {i,0,n}] == 10
T>0
I tried (ignoring T>0) to use NSolve, which didn't work. I guessed the
problem is that the summation limit depends on T which is also a part of the
summand. However, Mathematica succefully solves the simpler Sum[n, {i, 0,
n}] == 2. What is the essence of the problem? How can I solve it?
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