(Fall 1999) A system has been partially modeled using a bond graph and characteristics as shown. a. Annotate the diagram as needed. Note that the capacitance is linear while the resistance is nonlinear. b. Find the (nonlinear) state differential equations. From the bond graph one finds, ( ) R R V Q P = d . From the resistance characteristic 2 4 /10 R R Q P = - + + . From the bond graph and capacitance characteristic curve 00/ 25 R P P V C P V =-=-. Combining ( ) ( )0 2 4 /10 2 4 25 /10 R R R V Q P P P V = = - + + = - + +-d . Thus, 02 4 /10 2.5 V P V = - + +-d . c. Determine the equilibrium state(s) of the system if 20 50N/m P = . Setting the time changing variable to zero, gives 002 4 /10 2.5 P V = - + +-. Substitution and initial Reduction, first gives
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