# Bode Plot

Time Limit: 1 Second Memory Limit: 32768 KB

**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.

## 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, 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 1.000Submit

Source: Greater New York 2001