We define transfer function H(s) as a ratio of the Laplace transform of system output (or response)(s) to the Laplace transform of the input(or forcing function)v(s) when all initial conditions are zero, then

We consider each term of the Fourier aeries representing the voltage as a single source. The equivalent impedance of the network at no is used to compute the current at that harmonic. XL(n) =noL and XC() =-1/noC The sum of these individual responses is the total response i

We define the ratio of the phasor voltage to the phasor current as impedance

The complete response is written as the sum of the forced and the natural response, and the initial conditions are then determined and applied to the complete response to find the values of the constants

We define the unit-step forcing function as a function which is zero for all values of argument which are less than zero and which is unity(1) for all positive values of its argument

Let us first define a linear element as passive element that has a linear voltage-current relationship

A point at which two or more elements have common connection is called node(节点). Suppose that we start at one node in a network and move through a simple element to the node at the other..., if no node was encountered more than once, then the set of nodes and elements that we have passed hrough is defined as path(路径)

2.1 SOME NOTATION 1. The Summation Notation X, =X1++...+n can be abbreviated as:Σx,orΣx 2. Properties of the Summation Operator

Working on a vacuum manifold: See LLP chapter 9.2 for an excellent discussion on working with air-sensitive reagents, including how to use a two-way manifold. De-gassing solvents: The best way to remove water and oxygen from a solvent is to distill it over an appropriate drying agent (such as sodium). This can sometimes be a lengthy (and dangerous)task. Since we

A pendulum is a rigid body suspended from a fixed point (hinge) which is offset with respect to the body's center of mass. If all the mass is assumed to be concentrated at a point, we obtain the idealized simple pendulum. Pendulums have played an important role in the history of dynamics. Galileo identified the pendulum as the first example of synchronous motion, which led to the first successful clock developed