The Heaviside function Help

In summary, the conversation discusses using the Green's function to find the solution for L[y]=H(t-pi/2)sint=q(t) with the initial condition y(0)=0. The person is stuck on how to incorporate the Heaviside function into the general solution and wonders if it is related to the fact that the Heaviside function is the integral of the Delta Dirac function. They ask for help and clarification. The conversation also mentions finding the Green's function and the solution y(t) in terms of the Green's function.
  • #1
sassie
35
0

Homework Statement



Find the solution for

L[y]=H(t-pi/2)sint=q(t)
y(0)=0

by using the Green's function.

Homework Equations


The Attempt at a Solution



My problem is that I'm stuck with how to get the Heaviside into the required general solution. Is it anything to do with the fact that the Heaviside function is the integral of the Delta Dirac function? Help. I'm really stuck!
 
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  • #2
sassie said:

Homework Statement



Find the solution for

L[y]=H(t-pi/2)sint=q(t)
y(0)=0

by using the Green's function.

Homework Equations


The Attempt at a Solution



My problem is that I'm stuck with how to get the Heaviside into the required general solution. Is it anything to do with the fact that the Heaviside function is the integral of the Delta Dirac function? Help. I'm really stuck!
Did you find the Green's function? What is the solution y(t) in terms of the Green's function?
 

1. What is the Heaviside function and how is it used?

The Heaviside function, also known as the unit step function, is a mathematical function that is defined as 0 for negative input values and 1 for positive input values. It is commonly used in engineering and physics to model systems that have a sudden change or "step" in behavior.

2. How is the Heaviside function related to the Dirac delta function?

The Heaviside function and the Dirac delta function are closely related, as the derivative of the Heaviside function is the Dirac delta function. This means that the Heaviside function can be used to represent the integral of the Dirac delta function.

3. Can the Heaviside function be generalized to higher dimensions?

Yes, the Heaviside function can be extended to multiple dimensions, resulting in the Heaviside step function. This function is defined as 0 for negative input values and 1 for positive input values in each dimension, creating a "step" in multiple dimensions.

4. How is the Heaviside function used in electrical engineering?

In electrical engineering, the Heaviside function is often used to model the behavior of electrical circuits with sudden changes, such as turning a switch on or off. It is also used in the Laplace transform to simplify the analysis of electrical systems.

5. Is the Heaviside function the same as a "unit step" function?

Yes, the Heaviside function is often referred to as a "unit step" function because it is equal to 1 for positive input values and 0 for negative input values, creating a "step" from 0 to 1 at the origin. However, some sources may use the term "unit step" to refer to a different function with similar properties.

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