Complex Frequency S, S* and S1, S1*?

In summary, the conversation discusses determining the complex frequency S for a given function, g(t). The attempt at a solution involves using the equations for finding the voltage, v(t), and results in four complex frequency terms, s1, s2, s3, and s4. However, these terms are not in standard form and it is unclear how to handle them.
  • #1
korbear
6
1
Complex Frequency S, S* and S1, S1*?

Homework Statement


Figure out what the complex frequency S is.
g(t)=[4e^(-2t)-e^(-t)]cos(4t-95degree)

Homework Equations


v(t)=K1e^(s1t)+K2e^(s2t)

The Attempt at a Solution


I got,
v(t)=K1e^s1 + K1e^s2 - K2e^s3 - K2e^s4
Which looks very messy.

Turns out it gives me,
s1=-2+j4, s2=-2-j4, s3=-1+j4 and s4=-1-j4
Which is not a standard form, and I have no idea how to handle four terms...

Much appreciate any inputs!:tongue:
 
Physics news on Phys.org
  • #2


It's right, I figured it out!
 

1. What are Complex Frequency S, S*, and S1, S1*?

Complex Frequency S, S*, and S1, S1* are mathematical representations of the frequency response of a system. They are used to analyze signals and systems in various fields such as engineering, physics, and mathematics.

2. How are Complex Frequency S, S*, and S1, S1* related to each other?

S and S* are complex conjugates of each other, meaning they have the same real part but opposite imaginary parts. Similarly, S1 and S1* are also complex conjugates of each other. They are related through the Laplace transform, which is a mathematical tool used to analyze signals and systems.

3. What is the significance of the complex conjugate property in Complex Frequency S, S*, and S1, S1*?

The complex conjugate property is important in Complex Frequency S, S*, and S1, S1* as it allows us to simplify complex mathematical expressions and make calculations easier. It also helps us to visualize the frequency response of a system in a more intuitive way.

4. How are Complex Frequency S, S*, and S1, S1* used in practical applications?

Complex Frequency S, S*, and S1, S1* are used in various fields such as control systems, signal processing, and circuit analysis. They are used to analyze the stability and performance of systems, design filters and controllers, and model real-world phenomena.

5. Are there any limitations to using Complex Frequency S, S*, and S1, S1* in signal and system analysis?

While Complex Frequency S, S*, and S1, S1* are powerful tools in analyzing signals and systems, they do have some limitations. They can only be used for linear time-invariant systems and may not accurately represent non-linear or time-varying systems. Additionally, they may require advanced mathematical knowledge to fully understand and interpret the results.

Similar threads

A standard form of Complex Frequency can only have two terms?
    • Electrical Engineering
Replies
2
Views
1K
VHDL coding -- Design a component that uses a 4-to-1 multiplexer
    • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
Engineering Overdamped Series RLC Circuit Transient Response
    • Engineering and Comp Sci Homework Help
Replies
2
Views
9K
Water droplet coalescence - prove S < S1 + S2
    • Precalculus Mathematics Homework Help
Replies
32
Views
3K
Engineering How Do You Determine Transient Response Voltages in a Series RLC Circuit?
    • Engineering and Comp Sci Homework Help
Replies
2
Views
3K
Arrays and recursion in mips assembly language
    • Engineering and Comp Sci Homework Help
Replies
1
Views
6K
Marginal stabilty in s domain
    • Other Physics Topics
Replies
1
Views
953
How far does the block slide? (work, spring, incline)
    • Introductory Physics Homework Help
Replies
4
Views
1K
Mechanics problems involving velocity,acceleration and gravity
    • Introductory Physics Homework Help
Replies
12
Views
3K
Simulating System of Masses Connected by Springs
    • Engineering and Comp Sci Homework Help
Replies
14
Views
5K

Hot Threads

Recent Insights

Back
Top