# Bode Plot

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

## Description

Problem

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 ω t and v2 = VR cos ( ω t + θ ) where VS is the voltage of the source, ω is the frequency (in radians per second), and t is time. VR is the magnitude of the voltage drop across the resistor, and θ is its phase. You are to write a program to determine VR for different values of ω. 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.

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, ω.

## 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 

None

## Source

Greater New York 2001