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Re: Three masses and four springs

• To: mathgroup at smc.vnet.net
• 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]

• References:
  • Three masses and four springs
    • From: Robert Jenkins <dale.jenkins8@gmail.com>