Simple step function, Laplace transform

In summary, to find y(t) for a system characterized by the equation y' + 3y = r', the inverse Laplace transform of Y(s) must be taken when the input r(t) is u(t) - u(t-1). The Laplace transform integral, the Laplace transform of a derivative, the transfer function of the system, and the impulse response can be used to solve this problem. If unsure, seek further clarification.
  • #1
i_am_stupid
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Homework Statement


A system is characterized by the equation y' + 3y = r' .

When the input is r(t) = u(t) - u(t-1), find y(t) by taking the inverse Laplace transform of Y(s).

Homework Equations


The Laplace transform integral
The Laplace transform of a derivative sF(s) - f(0)

The transfer function of the system Q = s/s+3

The impulse response qimp(t) = δ(t) - 3e-3t

The Attempt at a Solution


I'm really not sure what to do here. It seems like it should be simple enough but I feel like I am not understanding the question correctly. Any hints?
 
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  • #2
Nevermind, got it.
 

Related to Simple step function, Laplace transform

1. What is a simple step function?

A simple step function is a mathematical function that takes the value of 0 for all negative inputs and 1 for all positive inputs. It is represented as a straight line with a discontinuity at the point of interest.

2. What is the Laplace transform of a simple step function?

The Laplace transform of a simple step function is 1/s, where s is the complex variable. This transform is used to convert the original function into a new function in the complex domain, making it easier to solve certain mathematical problems.

3. How is the Laplace transform of a step function used in real-world applications?

The Laplace transform of a step function is commonly used in engineering and physics to solve differential equations and analyze dynamic systems. It is also used in signal processing to study the behavior of signals over time.

4. What is the inverse Laplace transform of a step function?

The inverse Laplace transform of 1/s is a step function, which can be represented as a unit step or Heaviside function. This function is commonly used to model physical systems that have a sudden change in behavior at a specific point in time.

5. Can a simple step function have multiple steps?

Yes, a simple step function can have multiple steps, each representing a different discontinuity in the function. This can be useful in modeling complex systems that have multiple changes in behavior over time.

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