Simplifying and Solving Step Functions with Laplace Transform

  • Thread starter EvLer
  • Start date
  • Tags
    Functions
In summary, the conversation discusses a function, f(t), that is represented by a pulse-type waveform. The goal is to simplify the function and find its Laplace transform. The conversation also clarifies the definition of the u function and determines the values of f(t) in different intervals. Finally, it is mentioned that the function can be represented as u(t-1) - u(t-5) and the Laplace transform can be easily found from this representation.
  • #1
EvLer
458
0
ARGH! they drive me crazy! and our TA does not have office hrs this week :eek:

what does this thing look like?

f(t) = 10 u(t-1)u(5-t)u(t) ?

and what is the strategy to determine it? actually i need a laplace transform of it, but I need to simplify it first, then maybe i can do it by myself.

Thanks in advance.
 
Engineering news on Phys.org
  • #2
I'm guessing the u function is 1 when it's argument is greater than or equal to 0, and 0 otherwise? So f(t) is 10 when (t-1) > 0, (5-t) > 0, and t > 0, and f(t) is 0 otherwise.

t > 1
t < 5
t > 0

simplifies to:

t in [1, 5]

So f(t) = 10 when t in [1, 5] and f(t) = 0 otherwise. Of course, if I've got this step function wrong, then you'll have to make appropriate adjustments, but there you go.
 
  • #3
Oh, I see... that's a little more understandable. Thanks much! Oh, yeah, sorry forgot to define step, your definition is correct.
Now, since this is a pulse-type waveform, I can represent it as u(t-1) - u(t-5) and the appropriate laplace transform is simple.
 

1. What is a step function?

A step function is a mathematical function that has a constant value within specific intervals and changes abruptly from one value to another at the boundaries of these intervals.

2. What are the applications of step functions?

Step functions are commonly used in economics, physics, engineering, and computer science to model discontinuous phenomena such as population growth, pricing strategies, and signal processing.

3. How is a step function different from a continuous function?

A step function is discontinuous, meaning there are abrupt changes in the function's value at specific points, while a continuous function has a smooth, unbroken graph with no abrupt changes. Additionally, a step function can only take on a finite number of distinct values, while a continuous function can take on an infinite number of values within a given interval.

4. What is a unit step function?

A unit step function, also known as the Heaviside step function, is a specific type of step function that has a value of 0 before a certain point and a value of 1 after that point. It is commonly used in physics and engineering to model the response of a system to a sudden input or stimulus.

5. Can step functions be used to model real-life situations?

Yes, step functions can be used to model real-life situations that involve discrete changes or sudden transitions. For example, a step function can be used to model the changing price of a product depending on certain factors, or the growth of a population after a certain event.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
4
Views
989
  • Differential Equations
Replies
17
Views
807
  • Differential Equations
Replies
5
Views
1K
Replies
10
Views
2K
Replies
7
Views
2K
Replies
2
Views
689
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
956
  • Differential Equations
Replies
2
Views
2K
  • Differential Equations
Replies
1
Views
588
Back
Top