Coupled Oscillators. Description. Easy Java Simulations step-by-step series of examples

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1 Easy Java Siuations step-by-step series of eapes Coupe Osciators page of 8 Coupe Osciators Description We siuate the otion of two partice asses connecte by three springs. One spring connects the two asses an two other springs connect the to the outer was. If,, an 3 are the eastic constants of the springs fro eft to right in the iage, which both have a ength at equiibriu, an an the asses of the eft an right partices, respectivey, the equations of the positions not ispaceent! of the asses an are given by the coupe syste of secon-orer ifferentia equations: 3 t t + = + = Introucing aitiona variabes for the horizonta veocities of the partices, v an v, we can write this syste as an equivaent syste of four first-orer ifferentia equations: 3 t v v t t v v t + = = + = = This foruation is reay for Ejs eitor of ifferentia equations.

2 Easy Java Siuations step-by-step series of eapes Moe Variabes We nee a rather ong ist of oube variabes whose eanings have been epaine above. Initiaization For the initiaization we write the sipe coe: This coe just freezes the partice at the given positions an the ine: _view.resettraces; cears the traces of the ispaceents. Evoution The evoution uses a page of ODEs: Coupe Osciators page of 8

3 Easy Java Siuations step-by-step series of eapes We choose the Euer-Richarson secon-orer etho which is powerfu enough for these rather we-behave equations. But there is no reason why a ore powerfu Runge-Kutta etho can be seecte instea. Constraints No constraints are require. Custo coe No custo coe require. See however the Action property of the Specia oes: buttons in the view. View The view starts with the copoun eeent base on a rawing pane with a efaut partice, but we wi nee to ae severa changes to it. First, we repace the centra rawing pane with a siper Pane container with Borer ayout which wi ho a rawing pane an a potting pane, both with ifferent sizes. See the etai of the Tree of Eeents in the figure beow: Coupe Osciators page 3 of 8

4 Easy Java Siuations step-by-step series of eapes The Up position of centerpane I soccupie by a rawing pane which wi contain the partices an springs. We have ajuste its etrees so that the partices oo ie circes. The properties of the rawing pane an its chiren are the foowing: Coupe Osciators page 4 of 8

5 Easy Java Siuations step-by-step series of eapes Note: The iportant figure in the 00,00 size is the secon 00 which inicates the iniu height require by the pane. The parent centerpane wi stretch the rawing pane in the horizonta iension as neee. Coupe Osciators page 5 of 8

6 Easy Java Siuations step-by-step series of eapes Notice the Action properties of both partices. The On Drag property is neee to ae sure the partices o not ove in the vertica irection. The potting pane beow the previous rawing pane occupies the center position of centerpane. The potting pane is rather stanar, has autoscaing, an hosts two Trace eeents. One for each of the ispaceents. The property pane of these are: The Sip property is set to so that the pots raw on point after two evoution steps. Coupe Osciators page 6 of 8

7 Easy Java Siuations step-by-step series of eapes We now show a etai of the Tree of Eeents of the rest of the view The eeents use in these two panes are rather stanar. It is interesting to see the Action properties of the oebutton, oebutton, an echangebutton buttons. These contain the foowing coe, respectivey: // Moe button = 0.7*; =.3*; = = 3 =.0; initiaize; // Moe button = 0.7*; =.7*; = = 3 =.0; initiaize; // Echange of energies button = 0.7*; = *; = 3 =.0; = 0.; initiaize; Running the siuation Coupe Osciators page 7 of 8

8 Easy Java Siuations step-by-step series of eapes Here is a sape eecution using the paraeters an initia conitions of oe : Author Francisco Esquebre Universia e Murcia, Spain Juy 007 Coupe Osciators page 8 of 8