Different type of differential question most ppl used to

In summary, the conversation discusses a differential equation and the need to determine the right hand side of the equation. The complementary solution and particular solution are given, and the unit step function can be ignored. The conversation also mentions the characteristic equation and suggests putting the particular solution into the homogeneous equation to determine the right side.
  • #1
squirby
1
0
hey guys. just wondering if anyone can help me out, this is a different type of question most ppl are used to.

"For a system, it is given that the complementary solution is 8exp(-3t)u(t).
The particular solution for the system is cos(4t)u(t). determine, in its simplest form, the forcing function, f(t), applied to the system"

basically, they are asking for you to determine the right hand side of a differential equation, and they haven't given us the left hand side. we can ignore u(t),it's the unit step function and since we are only solving for t greater than zero this can be ignored.

just wondering, can anyone give me steps to solving this? I'm desperate... can't find a similar type of question anywhere. thanks heaps for any input guys!
 
Physics news on Phys.org
  • #2
Well, if exp(-3t) is a solution of the homogeneous equation then its characteristic equation would be r + 3 = 0 so the homogeneous equation would be:

y' + 3y = 0

Now put y = cos(4t) in that equation to see what the right side needs to be.
 

FAQ: Different type of differential question most ppl used to

What is a differential question?

A differential question is a type of question that compares two or more variables and examines how they change in relation to each other. It is used to analyze and understand the relationship between different factors.

What are the different types of differential questions?

There are three main types of differential questions: comparative, causal, and predictive. Comparative questions compare different groups or variables, causal questions examine cause-and-effect relationships, and predictive questions use existing data to make predictions about future outcomes.

How are differential questions used in scientific research?

Differential questions are commonly used in scientific research to investigate relationships between variables and to make predictions about future outcomes. They allow researchers to identify patterns and trends in data and to better understand the underlying mechanisms of a phenomenon.

What are some examples of differential questions?

Examples of differential questions include "How does gender affect income levels?", "What is the relationship between exercise and heart health?", and "Can we predict the stock market based on past trends?" These questions all compare different variables and seek to understand their relationship.

What are some common pitfalls when using differential questions?

One common pitfall when using differential questions is failing to control for confounding variables, which can distort the relationship between the variables being studied. Another pitfall is making assumptions about causality based on correlation, which may not accurately reflect the true relationship between variables. It is important to carefully design and analyze research using differential questions to avoid these pitfalls.

Similar threads

I On vibrating string and differentiating infinite sum
Replies
7
Views
1K
I Verifying properties of Green's function
Replies
1
Views
2K
I Can I Differentiate Both Sides to Solve y in y^2=ln(1-y^2)?
Replies
2
Views
2K
MHB Help with a question (Bernoulli General solution)
Replies
8
Views
2K
I On error estimates of approximate solutions
Replies
1
Views
2K
I Separation of Variables, but not equal to constant
Replies
3
Views
2K
I Where did this substitution technique go wrong?
Replies
27
Views
3K
I Runge-Kutta 4 w/ some sugar on the top: How to do error approximation?
2
Replies
65
Views
4K
I On the approximate solution obtained through Euler's method
Replies
1
Views
2K
I Feynmann's connection machine model
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top