$3.$ For this project$$s program, you will derive subordinate classes from a base class, and you will create a class that provides static methods that are not provided in Java$$s Math class. These new methods will perform addition, subtraction, multiplication, and division of $$complex$$ numbers $$ numbers that have two components, a $$real$$ double value, and an $$imaginary$$ double value that is orthogonal to it$.$ Complex numbers enable you to analyze a system having time$-$varying sinusoidal signals without having to do a simulation.

Your task is to write a program that calculates the steady$-$state currents in a two$-$loop electric circuit that has an arbitrary combination of discrete resistors, inductors, capacitors, and voltage sources in the legs of the circuit. For any one solution, assume the voltage source$($s$)$ oscillate at a particular frequency, but write the program so that after a user has defined the circuit, the calculation can be repeated with everything the same except for the frequency. In the driver, provide a loop that steps through the frequencies $16$ Hz$,16*$ sqrt$(2)$ Hz$,32$ Hz$,32*$ sqrt$(2)$ Hz$,...46341$ Hz$,$ and at each frequency, display $10*$ log$10($outputWatts$)$ for two selected resistors in the circuit, by printing W or T at a horizontal distance that is proportional to the log of the output power.

Demonstrate the program for the specific example of a loudspeaker crossover network that splits an audio signal between woofer $($low$-$frequency$)$ and tweeter $($high$-$frequency$)$ loudspeakers. Here$$s the circuit, and the values to use for your demonstration:

For the voltage source, use V$0=4$ volts. For the resistors, use the typical audio values of R$0=$ Rw $=$ Rt $=8$ Ohms. For the woofer leg$$s inductor, use Lw $=1\mathrm{.}3$ millihenrys. For the tweeter leg$$s capacitor use Ct $=10$ microfarads. This results in a crossover frequency of fc $=1/(2\backslash$pi $*$ sqrt$($LC$))=987$ Hz$.$

The current through the tweeter loudspeaker $($the Rt resistance$)$ is the second loop current, I$1.$ The current through the woofer loudspeaker $($the Rw resistance$)$ is the difference between the two loop currents, Iw $=$ I$0$ I$1.($If we had drawn the second loop current in the counter$-$clockwise direction, the current through the woofer loudspeaker would have been the sum of the two loop currents.$)$ The power into either one of the loudspeakers is the square of the magnitude of the net current into that loudspeaker times the resistance of that loudspeaker. The value $10*$ log$10($loudspeaker power in watts$)$ is called the decibel level, and that is what your program will display, like this:

Sample session:

Total number of circuit elements$=5$

Enter resistor $($r$),$ capacitor$($c$),$ or inductor$($i$)$: r

Enter component name: R$0$

Enter value in Ohms: $8$

Enter resistor $($r$),$ capacitor$($c$),$ or inductor$($i$)$: i

Enter component name: Lw

Enter value in Henrys: $1\mathrm{.}3$e$-3$

Enter resistor $($r$),$ capacitor$($c$),$ or inductor$($i$)$: r

Enter component name: Rw

Enter value in Ohms: $8$

Enter resistor $($r$),$ capacitor$($c$),$ or inductor$($i$)$: c

Enter component name: Ct

Enter value in Farads: $20$e$-6$

Enter resistor $($r$),$ capacitor$($c$),$ or inductor$($i$)$: r

Enter component name: Rt

Enter value in Ohms: $8$

Loop number $0$:

Voltage source? $($y$,$n$)$: y

Enter magnitude in volts: $4\mathrm{.}0$

Enter angle in degrees: $0\mathrm{.}0$

Coefficient number $0$:

Number of components $($minus for opposing current$)$: $3$

Enter component name: R$0$

Enter component name: Lw

Enter component name: Rw

Coefficient number $1$:

Number of components $($minus for opposing current$)$: $-2$

Enter component name: Lw

Enter component name: Rw

Loop number $1$:

Voltage source? $($y$,$n$)$: n

Coefficient number $0$:

Number of components $($minus for opposing current$)$: $-2$

Enter component name: Lw

Enter component name: Rw

Coefficient number $1$:

Number of components $($minus for opposing current$)$: $4$

Enter component name: Rw

Enter component name: Lw

Enter component name: Ct

Enter component name: Rt

Enter woofer resistance name: Rw

Enter tweeter resistance name: Rt

frequency decibels

$($Hz$)-40-30-20-100$

$16.$T $...$ W $.$

$23.$ T $...$ W $.$

$32.$ T $...$ W $.$

$45.$ T $..$ W $.$

$64..$ T $..$ W $.$

$91..$ T $..$ W $.$

$128..$ T$..$ W $.$

$181...$ T $.$ W $.$

$256...$ T $.$ W $.$

$362...$ T $.$ W $.$

$512...$ T W $.$

$724....$ T W $.$

$1024....$ W $.$

$1448....$ W T $.$

$2048...$ W T $.$

$2896.$