Following an example. Implies L{2du/dt+1}=2s+1. I'm Confused.

In summary, the conversation is about a confusion regarding an example in a handout on transfer functions. The person is questioning the author's use of notation and the resulting Laplace transforms. They suggest that the author may be using "u" to represent the unit step function and the derivative of this function is the dirac delta function, which would explain the presence of 2s in the Laplace transform. They also mention that derivatives in the t-space result in multiplication by s in the s-space and integration in the t-space results in division by s in the s-space.
  • #1
james_a
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So I am reading a handout on transfer functions, and I got to this one example that doesn't seem right to me - which usually means I'm missing something.

It looks like this:
Screenshot_02092017_06_09_00_PM.png


My understanding is that the numerator in H(s) is supposed to be the laplace transform of the input for the differential equation, so N(s)=L{2du/dt+1}.

I'm not sure how the author got {2du/dt+1}=2s+1. Isn't L{1} supposed to be 1/s? And I'm not sure what to make of L{2du/dt}.

Maybe the author is using "u" to notate the unit step function, so du/dt would be the dirac delta function δ(t), and L{2δ(t)}=2 . Still, where does 2s come from? Why wouldn't they have just written 2δ(t) in the first place? And that still doesn't explain how, apparently, according to the author L{1}=1.

Any clarification is greatly appreciated.
 
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  • #2
A derivative in the t-space gives multiplication by s in the s-space. And integration in the t-space gives division by s in the s-space.

(For proofs, see

and
 
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FAQ: Following an example. Implies L{2du/dt+1}=2s+1. I'm Confused.

1. How do you solve an equation that involves following an example?

To solve an equation by following an example, you first need to understand the given example and the steps involved in solving it. Then, you can apply the same steps to solve the given equation.

2. What does "L" stand for in the equation L{2du/dt+1}=2s+1?

In this equation, "L" represents a linear operator, which is a mathematical function that maps one vector space to another.

3. What is the purpose of the "2" in front of "du/dt" in the equation?

The "2" in front of "du/dt" represents the coefficient of the variable "u" in the equation. It is used to indicate the relationship between "u" and the other variables in the equation.

4. How do you determine the value of "u" in the equation L{2du/dt+1}=2s+1?

To determine the value of "u", you need to isolate it on one side of the equation by performing algebraic operations. Once "u" is isolated, you can solve for its value.

5. What is the significance of the constant "1" in the equation L{2du/dt+1}=2s+1?

The constant "1" in this equation represents a fixed value and is used to balance the equation. It is important to include constants in equations to accurately represent real-life situations and to make the equation solvable.

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