       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)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-outx@smc.vnet.net
• Delivered-to: mathgroup-newsendx@smc.vnet.net
• 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 == -1, x2 == 2, x3 == -1,
x1' == 0, x2' == 0, x3' == 0},
{x1[t], x2[t], x3[t]}, t] //
FullSimplify

{{x1[t] -> (1/2)*
((-1 + Sqrt)*
Cos[Sqrt[2 - Sqrt]*
t] - (1 + Sqrt)*
Cos[Sqrt[2 + Sqrt]*
t]),
x2[t] -> (1/2)*
((-(-2 + Sqrt))*
Cos[Sqrt[2 - Sqrt]*
t] + (2 + Sqrt)*
Cos[Sqrt[2 + Sqrt]*
t]),
x3[t] -> (1/2)*
((-1 + Sqrt)*
Cos[Sqrt[2 - Sqrt]*
t] - (1 + Sqrt)*
Cos[Sqrt[2 + Sqrt]*
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 == -1, x2 == 2, x1' == 0, x2' == 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 == -1, x2 == 2,
>   x3 == -1, x1' == 0, x2' == 0, x3' == 0}, {x1, x2, x3},
>   t]
>
>

```

• Prev by Date: Three masses and four springs
• Next by Date: Re: Tracking progress in ParallelDo
• Previous by thread: Three masses and four springs
• Next by thread: Re: Three masses and four springs