1002 -- Bode Plot
Time Limit :1000 MS Memory Limit :65536 KB
Accepts : 153 Submits : 213
User Accepts : 138 User Submits : 142
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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 v1 = VS cos w t and v2 = VR cos ( w t + 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 = i R where i 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.

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 VS, 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 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

 

Hint

Source

Greater New York 2001
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