Bode Plot - 1045

Bode Plot

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 13495		Accepted: 8523

DescriptionConsider the AC circuit below. We will assume that the circuit is in steady-state. Thus, the voltage at nodes 1 and 2 are given by v1 = VS coswt and v2 = VRcos(wt + q ) where VS is the voltage of the source, w is the frequency (in radians per second),and t is time. VR is the magnitude of the voltage drop across the resistor, and q is its phase.You are to write a program to determine VR for different values of w. You will need two laws of electricity to solve this problem. The first is Ohm's Law, which states v2 = iR wherei is the current in the circuit, oriented clockwise. The second is i = C d/dt (v1-v2) which relates the current to the voltage on either side of the capacitor. "d/dt"indicates the derivative with respect to t.InputThe input will consist of one or more lines. The first line contains three real numbers and a non-negative integer. The real numbers are VS, R, and C, in that order. The integer, n, is the number of test cases. The following n lines of the inputwill have one real number per line. Each of these numbers is the angular frequency, w.OutputFor each angular frequency in the input you are to output its corresponding VR on a single line. Each VR value output should be rounded to three digits after the decimal point.Sample Input

1.0 1.0 1.0 9
0.01
0.031623
0.1
0.31623
1.0
3.1623
10.0
31.623
100.0

Sample Output

0.010
0.032
0.100
0.302
0.707
0.953
0.995
1.000
1.000

分析：

此题的关键在于进行微积分的公式推导，其中涉及复合函数求导和三角函数的计算等问题，具体推导过程如下：

最后其实就是:VR = CRW*VS*sqrt(1/pow(CRW) + 1)

代码实现如下：