proj1045

Language: Default

Bode Plot

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 12040		Accepted: 7721

Description

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 = V_S coswt and v₂ = V_Rcos (wt + q ) where V_S is the voltage of the source, w is the frequency (in radians per second), and t is time. V_R is the magnitude of the voltage drop across the resistor, and q is its phase.

You are to write a program to determine V_R for different values of w. You will need two laws of electricity to solve this problem. The first is Ohm's Law, which states v₂ = iR 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 V_S, 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, w. 

Output

For each angular frequency in the input you are to output its corresponding V_R on a single line. Each V_R 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

Source

Greater New York 2001

 

 

公式推导：
V2=I.R=C.R.d/dt(Vs*cos(Wt)-Vr*cos(Wt+B))=Vrcos(wt+B)

C.R.W.(Vr.sin(wt+b)-Vs.sin(wt))=Vr*cos(wt+b)

令t=0化简得：   tan(b)=1/(C.R.W)-------------(1)
令wt+b=0化简得：Vr=C.R.W.Vs*sin(b)------------(2)
                sinb=sqrt(tanb^2/(1+tanb^2))---(3)

              设a=C.R.W
由(1),(2),(3)得：   Vr=a.Vs/sqrt(1+a^2)).

//公式推导：V2=iR=CR d/dt(Vs*cos(wt)-Vr*cos(wt+b))=Vrcos(wt+b)
//          CRw(sin(wt+b)-sin(wt))=Vr*cos(wt+b)
//          令t=0化简得：   tan(b)=1/(CRw)-------------(1)
//          令wt+b=0化简得：Vr=CRwVs*sin(b)------------(2)
//          由(1),(2)得：   Vr=CRwVs/sqrt(1+(CRw)^2))

#include <stdio.h>
#include <math.h>
int main()
{
	double vs,r,c,w,vr;
	int i,t;
	scanf("%lf %lf %lf %d",&vs,&r,&c,&t);
	for(i=1;i<=t;i++)
	{
		scanf("%lf",&w);
		vr=c*r*w*vs/sqrt(1+c*r*w*c*r*w);
		printf("%.3lf
",vr);
	}
	return 0;
}