How can I express r(t) usingDirac delta functionorHeaviside step function?

I know that Heaviside is the antiderivative of Dirac.

EDIT:

then i got

I believe that I have to use theFrequency shiftproperty to get rid of , but how?

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- May 9th 2012, 04:42 AMcristi92Differential equations using Laplace transforms

How can I express r(t) using**Dirac delta function**or**Heaviside step function**?

I know that Heaviside is the antiderivative of Dirac.

EDIT:

then i got

I believe that I have to use the**Frequency shift**property to get rid of , but how?

- May 9th 2012, 01:43 PMHallsofIvyRe: Differential equations using Laplace transforms
The Heaviside function, H(x), has the value 0 for x< 0, 1 for x> 0. Here, you have to move that "cut point" to x= 1 and reverse ">" and "<". We can do that using

H(1- x). When x< 1, 1- x> 1 so H(1- x)= 1. When x> 1, 1- x< 0 so H(1- x)= 0. You want 8sin(t) for t< 1, 0 for t> 1 so you want 8sin(t)H(1- t).

Quote:

EDIT:

then i got

I believe that I have to use the**Frequency shift**property to get rid of , but how?

- May 9th 2012, 02:17 PMcristi92Re: Differential equations using Laplace transforms
Thank you!