Bode Plot

Consider an alternating-current (AC) circuit that is assumed to be in steady state. The circuit consists of a voltage source, a capacitor, and a resistor. Node 1 is the source terminal, and node 2 is the point between the capacitor and the resistor. The voltages at the two nodes are

$v_1 = V_S \cos(\omega t), \qquad v_2 = V_R \cos(\omega t + \theta)$

where $V_S$ is the source voltage, $\omega$ is the angular frequency (in radians per second), and $t$ is time. $V_R$ is the magnitude of the voltage drop across the resistor, and $\theta$ is its phase.

Write a program that determines $V_R$ for different values of $\omega$. You will need two laws of electricity. The first is Ohm's Law: if $i$ is the current in the circuit, oriented clockwise, then $v_2 = iR$. The second relates the current to the voltages on either side of the capacitor: $i = C \dfrac{d}{dt}(v_1 - v_2)$, where $\dfrac{d}{dt}$ denotes the derivative with respect to $t$.

The input consists 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 queries. Each of the following $n$ lines contains a single real number, the angular frequency $\omega$.

For each angular frequency, output the corresponding $V_R$ on its own line. Round each $V_R$ value to three digits after the decimal point.