Re: Three masses and four springs

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• Subject: [mg132600] Re: Three masses and four springs
• From: dale.jenkins8 at gmail.com
• Date: Thu, 17 Apr 2014 05:10:36 -0400 (EDT)
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• References: <20140416074027.11A846A2B@smc.vnet.net> <CAEtRDSd9rg8t6X5=+wbqdqJzsPFfEEaShDR0v_7JVy1mtWXfPg@mail.gmail.com>

```Thanks a lot. Much appreciated.

RJ

From: Bob Hanlon
Sent: Wednesday, April 16, 2014 3:07 PM
To: Robert Jenkins
Cc: MathGroup
Subject: [mg132600] Re: Three masses and four springs

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]

```

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