Bode Plot

Description

Consider 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 v
₁ = V
_S coswt and v
₂ = V
_Rcos (wt + q ) where V
_S is the voltage of the source, w is the frequency (in radians per second), and t is time. V
_R is the magnitude of the voltage drop across the resistor, and q is its phase.

You are to write a program to determine V
_R for different values of w. You will need two laws of electricity to solve this problem. The first is Ohm’s Law, which states v
₂ = iR where i is the current in the circuit, oriented clockwise. The second is i = C d/dt (v
₁-v
₂) which relates the current to the voltage on either side of the capacitor. “d/dt”indicates the derivative with respect to t.

Input

The input will consist of one or more lines. The first line contains three real numbers and a non-negative integer. The real numbers are V
_S, R, and C, in that order. The integer, n, is the number of test cases. The following n lines of the input will have one real number per line. Each of these numbers is the angular frequency, w.

Output

For each angular frequency in the input you are to output its corresponding V
_R on a single line. Each V
_R 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

Source

Greater New York 2001   分析：年轻态健康品——水  

 1 /*
 2 1.0 1.0 1.0 9
 3 0.01
 4 0.031623
 5 0.1
 6 0.31623
 7 1.0
 8 3.1623
 9 10.0
10 31.623
11 100.0
12  */
13 
14 #include <stdio.h>
15 #include <math.h>
16 
17 #define MAX_NUM 50
18 
19 int n;
20 double Vs, R, C;
21 double w[MAX_NUM], Vr[MAX_NUM];
22 
23 void GetData()
24 {
25     int i = 0;
26     scanf("%lf %lf %lf %d", &Vs, &R, &C, &n);
27     for(i=0; i<n; i++)
28     {
29         scanf("%lf", &w[i]);
30     }
31 }
32 
33 void Calc()
34 {
35     int i = 0;
36     for(i=0; i<n; i++)
37     {
38         Vr[i]=C*R*w[i]*Vs / sqrt(1 + pow(C*R*w[i], 2));
39     }
40 }
41 
42 void PrintResult()
43 {
44     int i = 0;
45     for(i=0; i<n; i++)
46     {
47         printf("%.3f\n", Vr[i]);
48     }
49 }
50 
51 int main()
52 {
53     GetData();
54     Calc();
55     PrintResult();
56     return 0;
57 }