How to change the system in 4x4 system of first-order equations? [duplicate]












0












$begingroup$



This question already has an answer here:




  • How to change the system in four first order equations?

    2 answers




Consider the coupled spring-mass system with a frictionless table, two masses $m_1$ and $m_2$, and three springs with spring constants $k_1, k_2$, and $k_3$ respectively. The equation of motion for the system are given by:



$y_1''=-frac{(k_1+k_2)}{m_1}y_1+frac{k_2}{m_1}y_2$



$y_2''=frac{k_2}{m_2}y_1-frac{(k_1+k_2)}{m_2}y_2$



Assume that the masses are $m_1 = 2$, $m_2 = 9/4$, and the spring constants are $k_1=1,k_2=3,k_3=15/4$.



a)use 4x4 system of first order equations to model this system of two second order equations. (hint: $x_1=y_1,x_2=y_2,x_3=y_1',x_4=y_2'$)










share|cite|improve this question









$endgroup$



marked as duplicate by LutzL differential-equations
Users with the  differential-equations badge can single-handedly close differential-equations questions as duplicates and reopen them as needed.

StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;

$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');

$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
Dec 5 '18 at 12:35


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.























    0












    $begingroup$



    This question already has an answer here:




    • How to change the system in four first order equations?

      2 answers




    Consider the coupled spring-mass system with a frictionless table, two masses $m_1$ and $m_2$, and three springs with spring constants $k_1, k_2$, and $k_3$ respectively. The equation of motion for the system are given by:



    $y_1''=-frac{(k_1+k_2)}{m_1}y_1+frac{k_2}{m_1}y_2$



    $y_2''=frac{k_2}{m_2}y_1-frac{(k_1+k_2)}{m_2}y_2$



    Assume that the masses are $m_1 = 2$, $m_2 = 9/4$, and the spring constants are $k_1=1,k_2=3,k_3=15/4$.



    a)use 4x4 system of first order equations to model this system of two second order equations. (hint: $x_1=y_1,x_2=y_2,x_3=y_1',x_4=y_2'$)










    share|cite|improve this question









    $endgroup$



    marked as duplicate by LutzL differential-equations
    Users with the  differential-equations badge can single-handedly close differential-equations questions as duplicates and reopen them as needed.

    StackExchange.ready(function() {
    if (StackExchange.options.isMobile) return;

    $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
    var $hover = $(this).addClass('hover-bound'),
    $msg = $hover.siblings('.dupe-hammer-message');

    $hover.hover(
    function() {
    $hover.showInfoMessage('', {
    messageElement: $msg.clone().show(),
    transient: false,
    position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
    dismissable: false,
    relativeToBody: true
    });
    },
    function() {
    StackExchange.helpers.removeMessages();
    }
    );
    });
    });
    Dec 5 '18 at 12:35


    This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.





















      0












      0








      0


      0



      $begingroup$



      This question already has an answer here:




      • How to change the system in four first order equations?

        2 answers




      Consider the coupled spring-mass system with a frictionless table, two masses $m_1$ and $m_2$, and three springs with spring constants $k_1, k_2$, and $k_3$ respectively. The equation of motion for the system are given by:



      $y_1''=-frac{(k_1+k_2)}{m_1}y_1+frac{k_2}{m_1}y_2$



      $y_2''=frac{k_2}{m_2}y_1-frac{(k_1+k_2)}{m_2}y_2$



      Assume that the masses are $m_1 = 2$, $m_2 = 9/4$, and the spring constants are $k_1=1,k_2=3,k_3=15/4$.



      a)use 4x4 system of first order equations to model this system of two second order equations. (hint: $x_1=y_1,x_2=y_2,x_3=y_1',x_4=y_2'$)










      share|cite|improve this question









      $endgroup$





      This question already has an answer here:




      • How to change the system in four first order equations?

        2 answers




      Consider the coupled spring-mass system with a frictionless table, two masses $m_1$ and $m_2$, and three springs with spring constants $k_1, k_2$, and $k_3$ respectively. The equation of motion for the system are given by:



      $y_1''=-frac{(k_1+k_2)}{m_1}y_1+frac{k_2}{m_1}y_2$



      $y_2''=frac{k_2}{m_2}y_1-frac{(k_1+k_2)}{m_2}y_2$



      Assume that the masses are $m_1 = 2$, $m_2 = 9/4$, and the spring constants are $k_1=1,k_2=3,k_3=15/4$.



      a)use 4x4 system of first order equations to model this system of two second order equations. (hint: $x_1=y_1,x_2=y_2,x_3=y_1',x_4=y_2'$)





      This question already has an answer here:




      • How to change the system in four first order equations?

        2 answers








      ordinary-differential-equations






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Dec 5 '18 at 11:33









      LTYLTY

      285




      285




      marked as duplicate by LutzL differential-equations
      Users with the  differential-equations badge can single-handedly close differential-equations questions as duplicates and reopen them as needed.

      StackExchange.ready(function() {
      if (StackExchange.options.isMobile) return;

      $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
      var $hover = $(this).addClass('hover-bound'),
      $msg = $hover.siblings('.dupe-hammer-message');

      $hover.hover(
      function() {
      $hover.showInfoMessage('', {
      messageElement: $msg.clone().show(),
      transient: false,
      position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
      dismissable: false,
      relativeToBody: true
      });
      },
      function() {
      StackExchange.helpers.removeMessages();
      }
      );
      });
      });
      Dec 5 '18 at 12:35


      This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.









      marked as duplicate by LutzL differential-equations
      Users with the  differential-equations badge can single-handedly close differential-equations questions as duplicates and reopen them as needed.

      StackExchange.ready(function() {
      if (StackExchange.options.isMobile) return;

      $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
      var $hover = $(this).addClass('hover-bound'),
      $msg = $hover.siblings('.dupe-hammer-message');

      $hover.hover(
      function() {
      $hover.showInfoMessage('', {
      messageElement: $msg.clone().show(),
      transient: false,
      position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
      dismissable: false,
      relativeToBody: true
      });
      },
      function() {
      StackExchange.helpers.removeMessages();
      }
      );
      });
      });
      Dec 5 '18 at 12:35


      This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
























          1 Answer
          1






          active

          oldest

          votes


















          0












          $begingroup$

          Introducing a whole new set of $x_i$ variables is somewhat confusing. Simpler to just introduce two new variables $y_3$ and $y_4$ where $y_3=y_1'$ and $y_4=y_2'$. So you now have:



          $y_1' = y_3$



          $y_2' = y_4$



          $y_3' = y_1'' = dots$



          $y_4'=y_2''= dots$






          share|cite|improve this answer









          $endgroup$




















            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            0












            $begingroup$

            Introducing a whole new set of $x_i$ variables is somewhat confusing. Simpler to just introduce two new variables $y_3$ and $y_4$ where $y_3=y_1'$ and $y_4=y_2'$. So you now have:



            $y_1' = y_3$



            $y_2' = y_4$



            $y_3' = y_1'' = dots$



            $y_4'=y_2''= dots$






            share|cite|improve this answer









            $endgroup$


















              0












              $begingroup$

              Introducing a whole new set of $x_i$ variables is somewhat confusing. Simpler to just introduce two new variables $y_3$ and $y_4$ where $y_3=y_1'$ and $y_4=y_2'$. So you now have:



              $y_1' = y_3$



              $y_2' = y_4$



              $y_3' = y_1'' = dots$



              $y_4'=y_2''= dots$






              share|cite|improve this answer









              $endgroup$
















                0












                0








                0





                $begingroup$

                Introducing a whole new set of $x_i$ variables is somewhat confusing. Simpler to just introduce two new variables $y_3$ and $y_4$ where $y_3=y_1'$ and $y_4=y_2'$. So you now have:



                $y_1' = y_3$



                $y_2' = y_4$



                $y_3' = y_1'' = dots$



                $y_4'=y_2''= dots$






                share|cite|improve this answer









                $endgroup$



                Introducing a whole new set of $x_i$ variables is somewhat confusing. Simpler to just introduce two new variables $y_3$ and $y_4$ where $y_3=y_1'$ and $y_4=y_2'$. So you now have:



                $y_1' = y_3$



                $y_2' = y_4$



                $y_3' = y_1'' = dots$



                $y_4'=y_2''= dots$







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Dec 5 '18 at 11:57









                gandalf61gandalf61

                8,841725




                8,841725















                    Popular posts from this blog

                    How to change which sound is reproduced for terminal bell?

                    Can I use Tabulator js library in my java Spring + Thymeleaf project?

                    Title Spacing in Bjornstrup Chapter, Removing Chapter Number From Contents