Solve Laplace Transform: y''+4y'+5y=3u^4(t)+7(t*u(t)*δ(t-1)

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In summary, the conversation is discussing the use of unit step functions and their notation, specifically u4(t). The original poster is unsure of how to solve for 3u^4(t) in a given problem and is seeking clarification on the notation and Laplace transform of u4(t). The other participant suggests forgetting about Laplace and focusing on understanding the notation first.
  • #1
okanas
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Homework Statement


could u help to find result? I don't know laplace of u^4(t)??


Homework Equations


y''+4y'+5y=3u^4(t)+7(t*u(t)*δ(t-1)


The Attempt at a Solution


The only one i couldn t found is 3u^4(t),,
 
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  • #2
Welcome to PF, okanas! :smile:

What is the exact definition of u(t)?
If you can say that, can you also say what u4(t) is?
(Forget about Laplace for now.)
 
  • #3
thank you Serena,
u4 denoted as a unit step function.

general piecewise (etc u(t-4)f(t-4) ) is easy to solve but power of function itselfs make it undone. Do you have any idea how we can deal with it?
 
  • #4
Huh? :confused:

I don't understand your question.
I don't see u(t-4)f(t-4) in your problem statement.

Are we still talking about u4(t)?
 
  • #5
:smile: yes we still talking about u4(t).

u(t) is unit step function.
 
  • #6
okanas said:
thank you Serena,
u4 denoted as a unit step function.
okanas said:
:smile: yes we still talking about u4(t).

u(t) is unit step function.
Which one is the unit step function, u(t) or u4(t)? Are you using some weird notation you haven't explained to us?

general piecewise (etc u(t-4)f(t-4) ) is easy to solve but power of function itselfs make it undone.
What is this supposed to mean? Please elaborate.
 
  • #7
Okay, so I believe it is defined as:
[tex]u(t)=\left\{\begin{matrix}0 & \textrm{ if } t < 0 \\ 1 & \textrm{ if } t \ge 0 \end{matrix} \right. [/tex]

What does that mean for u4(t)?
 
  • #8
okanas said:
general piecewise (etc u(t-4)f(t-4) ) is easy to solve but power of function itselfs make it undone. Do you have any idea how we can deal with it?

forget about this part,,

That's why i m asking you, what does u4(t) in ODE??
u(t)laplace--->1/s,,right??
So what is laplace u4(t)??
 
  • #9
If you'll bear with me for just a second, please forget about Laplace and the ODE for now.

Do you know what the notation u4(t) means?

Or if you really want the Laplace transform of it, can you give me the definition of the Laplace transform?
 

FAQ: Solve Laplace Transform: y''+4y'+5y=3u^4(t)+7(t*u(t)*δ(t-1)

What is a Laplace Transform?

A Laplace Transform is a mathematical tool used to convert a function from the time domain to the frequency domain. It is commonly used in engineering and physics to solve differential equations.

How do you solve a Laplace Transform?

To solve a Laplace Transform, you must first take the Laplace Transform of the given function. Then, use properties of the Laplace Transform, such as linearity and time shifting, to simplify the transformed function. Finally, use inverse Laplace Transform to convert the simplified function back to the time domain.

What does the notation y''+4y'+5y mean?

The notation y''+4y'+5y represents a second-order linear differential equation, where y represents the dependent variable and the primes represent the first and second derivatives of y with respect to t.

What is u(t) and δ(t-1) in the equation?

u(t) is the unit step function, which is equal to 1 for t>0 and 0 for t<0. δ(t-1) is the Dirac delta function, which is equal to 0 for all values of t except when t=1, where it is equal to infinity. In this equation, they are used to represent time shifts in the input function.

How can this Laplace Transform be applied in real-world situations?

Laplace Transform has many applications in engineering and physics, such as in circuit analysis, control systems, and signal processing. It can be used to model and predict the behavior of systems in these fields.

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