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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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  • 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]
>
>


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