Bode Plot

Time Limit: 2 Seconds
Memory Limit: 65536 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.

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.

**Example**

**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

**Output**

0.010

0.032

0.100

0.302

0.707

0.953

0.995

1.000

1.000

Source:

**Greater New York 2001**
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