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<CENTER><FONT color=blue size=+2>Bode Plot</FONT></CENTER>
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<CENTER><FONT color=green>Time limit:</FONT> 1 Seconds <FONT
color=green>Memory limit: </FONT>32768K </FONT><BR><FONT
color=green>Total Submit:</FONT> 527 <FONT color=green>Accepted
Submit:</FONT> 418 </CENTER>
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<P><B>Problem</B><BR><BR>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. </P>
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<P align=left>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.<BR><BR>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.</P>
<P align=left><BR><B>Output</B><BR><BR>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.</P>
<P align=left><BR><B>Example</B><BR><BR><B>Input</B><BR><BR>1.0 1.0 1.0
9<BR>0.01<BR>0.031623<BR>0.1<BR>0.31623<BR>1.0<BR>3.1623<BR>10.0<BR>31.623<BR>100.0<BR><BR><B>Output</B><BR><BR>0.010<BR>0.032<BR>0.100<BR>0.302<BR>0.707<BR>0.953<BR>0.995<BR>1.000<BR>1.000
<BR></P>
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<FONT color=green size=+1>Problem Source: </FONT><I>Greater New York 2001</I>
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