Re: Three masses and four springs
- To: mathgroup at smc.vnet.net
- Subject: [mg132598] Re: Three masses and four springs
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Thu, 17 Apr 2014 05:09:55 -0400 (EDT)
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- Delivered-to: l-mathgroup@wolfram.com
- Delivered-to: mathgroup-outx@smc.vnet.net
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- References: <20140416074027.11A846A2B@smc.vnet.net>
Use FullSimplify
DSolve[{
-2*x1[t] + x2[t] == x1''[t],
-2*x2[t] + x3[t] + x1[t] == x2''[t],
-2*x3[t] + x2[t] == x3''[t],
x1[0] == -1, x2[0] == 2, x3[0] == -1,
x1'[0] == 0, x2'[0] == 0, x3'[0] == 0},
{x1[t], x2[t], x3[t]}, t] //
FullSimplify
{{x1[t] -> (1/2)*
((-1 + Sqrt[2])*
Cos[Sqrt[2 - Sqrt[2]]*
t] - (1 + Sqrt[2])*
Cos[Sqrt[2 + Sqrt[2]]*
t]),
x2[t] -> (1/2)*
((-(-2 + Sqrt[2]))*
Cos[Sqrt[2 - Sqrt[2]]*
t] + (2 + Sqrt[2])*
Cos[Sqrt[2 + Sqrt[2]]*
t]),
x3[t] -> (1/2)*
((-1 + Sqrt[2])*
Cos[Sqrt[2 - Sqrt[2]]*
t] - (1 + Sqrt[2])*
Cos[Sqrt[2 + Sqrt[2]]*
t])}}
Bob Hanlon
On Wed, Apr 16, 2014 at 3:40 AM, Robert Jenkins <dale.jenkins8 at gmail.com>wrote:
> The instruction
> DSolve[{-2*x1[t] + x2[t] == x1''[t], -2*x2[t] + x1[t] == x2''[t],
> x1[0] == -1, x2[0] == 2, x1'[0] == 0, x2'[0] == 0}, {x1, x2}, t]
> produces a simple solution. But I am surprised to find the three-mass
> version produces a mass of complication. Have I made a mistake?
> DSolve[{-2*x1[t] + x2[t] == x1''[t], -2*x2[t] + x3[t] + x1[t] ==
> x2''[t], -2*x3[t] + x2[t] == x3''[t], x1[0] == -1, x2[0] == 2,
> x3[0] == -1, x1'[0] == 0, x2'[0] == 0, x3'[0] == 0}, {x1, x2, x3},
> t]
>
>
- References:
- Three masses and four springs
- From: Robert Jenkins <dale.jenkins8@gmail.com>
- Three masses and four springs