1、One-Dimension Wave,虞台文,Contents,The Wave Equation of Vibrating String Solution of the Wave Equation Discrete Time Traveling Wave,One-Dimension Wave,The Wave Equation of Vibrating String,Modeling of Vibrating String,Modeling of Vibrating String,Modeling of Vibrating String,1D Wave Equation,u(x, t) =
2、?,Boundary Conditions:,Initial Conditions:,One-Dimension Wave,Solution of theWave Equation,Separation of Variables,Assume,function of t,function of x,constant why?,Separation of Variables,Separation of Variables,Boundary Conditions:,Case 1:,Case 2:,G(t) 0,F(0) = 0 F(l ) =0,不是我們要的,Separation of Varia
3、bles,Boundary Conditions:,F(0) = 0, F(l) =0,F(x) = ?,Three Cases:,k,= 0, 0, 0,k = 0,a = 0 and b = 0,不是我們要的,k =2 (0),A = 0 B = 0,不是我們要的,k = p2 (0),k = p2 (0),Define,Any linear combination of Fn(x) is a solution.,k = p2 (0),Solution of Vibrating Strings,Initial Conditions,Initial Conditions,Initial Conditions,The Solution,Special Case: g(x)=0,Special Case: g(x)=0,Special Case: g(x)=0,Special Case: g(x)=0,Interpretation,Example,One-Dimension Wave,Discrete-Time Traveling Wave,Discrete-Time Simulation,
