不是我们要的

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1、One-DimensionWave虞台文ContentsTheWaveEquationofVibratingStringSolutionoftheWaveEquationDiscreteTimeTravelingWaveOne-DimensionWaveTheWaveEquationofVibratingStringModelingofVibratingString0luPQT1T2xx+xModelingofVibratingString0luPQT1T2xx+xModelingofVibratingString0luPQT1T2xx+

2、x1DWaveEquationu(x,t)=?BoundaryConditions:InitialConditions:0luOne-DimensionWaveSolutionoftheWaveEquationSeparationofVariablesAssumefunctionoftfunctionofxconstantwhy?SeparationofVariablesSeparationofVariablesBoundaryConditions:Case1:Case2:G(t)0F(0)=0F(l)=0不是我們要的SeparationofVar

3、iablesBoundaryConditions:F(0)=0,F(l)=0F(x)=?ThreeCases:k=0>0<0k=0BoundaryConditions:F(0)=0,F(l)=0F(x)=?a=0andb=0不是我們要的k=2(>0)BoundaryConditions:F(0)=0,F(l)=0F(x)=?A=0B=0不是我們要的k=p2(<0)BoundaryConditions:F(0)=0,F(l)=0F(x)=?k=p2(<0)BoundaryConditions:F(0)=0,F(l)=0F(x)=?DefineAnyl

4、inearcombinationofFn(x)isasolution.k=p2(<0)SolutionofVibratingStringsInitialConditionsInitialConditions0lf(x)InitialConditionsTheSolutionSpecialCase:g(x)=0SpecialCase:g(x)=00lf(x)SpecialCase:g(x)=00lf*(x)SpecialCase:g(x)=0Interpretationf*(x)f*(xct)f*(x+ct)Example0l0l0l0l0l0l0l

5、0lOne-DimensionWaveDiscrete-TimeTravelingWaveDiscrete-TimeSimulation12112111242