Check yourself Which of the following tanks has the largest time constant r?4 2 3. 4. 16
Check yourself 16
Example System:水箱 Formulate a mathematical description of this system. dri(t)ro(t)r1(t) dt T T Assume that the tank is initially empty,and then water enters at a constant rate ro(t)=1.Determine the output rate r(t). r1(t) time (seconds) 2 3 Please explain the shape of this curve mathematically 17
Example System: 水箱 17 Formulate a mathematical description of this system. Assume that the tank is initially empty, and then water enters at a constant rate r0 (t)=1. Determine the output rate r1 (t). Please explain the shape of this curve mathematically
Example System:水箱 Formulate a mathematical description of this system. dri(t)ro(t)r1(t) dt T T Assume that the tank is initially empty,and then water enters at a constant rate ro(t)=1.Determine the output rate r(t). r1(t) time (seconds) 2 3 Please explain the shape of this curve physically 18
Example System: 水箱 18 Formulate a mathematical description of this system. Assume that the tank is initially empty, and then water enters at a constant rate r0 (t)=1. Determine the output rate r1 (t). Please explain the shape of this curve physically
Another example system Although derived for a leaky tank,this sort of model can be used to represent a variety of physical systems. Water accumulates in a leaky tank. Charge accumulates in a capacitor. ro(t) m() r1(t) dh dt 0文0-1 analogous to do ii-io ii-io dt C 19
Another example system 19 Although derived for a leaky tank, this sort of model can be used to represent a variety of physical systems. Water accumulates in a leaky tank. Charge accumulates in a capacitor. analogous to
信号与系统：广泛的应用 The Signals and Systems approach has broad application: electrical,mechanical,optical,acoustic,biological,financial, mass spring system n(t) r2() tank system 2(t sound in sound out cell phone system 20
信号与系统：广泛的应用 • The Signals and Systems approach has broad application: electrical, mechanical, optical, acoustic, biological, financial, ... 20