Examples of using Over s squared in English and their translations into Arabic
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Colloquial
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Ecclesiastic
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Computer
And the Laplace transform of the cosine of at is equal to s over s squared plus a squared.
of cosine of t, I would get s over s squared plus 1.
Divide both sides by this, and we get y is equal to 1 over s squared-- And actually, let me make sure that that is right.
It's 1 over s squared. y is equal to 1 over s squared, times s squared, over s squared plus a squared.
so we have minus 1 over s squared, minus 1 over s squared, times 1.
So now we have s squared plus a squared, over s squared, times y is equal to this.
And the Laplace Transform of cosine of at is equal to s over s squared plus a squared.
So I get the Laplace Transform of y is equal to 2s plus 13, over s squared plus 5s plus 6.
So if you multiply the 1 out, you get 1/3 times 1 over s squared plus 1-- I'm just multiplying the 1 out-- minus 1/6-- these are all the 1's times the 1-- times 2 over s squared plus 4.
So we will have a minus a squared over s squared, times the integral from 0-- well, I said I'm just worrying about the indefinite integral right now, and we will evaluate the boundaries later. e to the minus st, sine of at, dt.
It's 1 over s squared plus 1 and then plus-- or minus actually, this is a minus-- minus the Laplace transfer of this thing, which was e to the minus 2 pi s over s squared plus 1.
And we get Y of s, the Laplace transform of Y is equal to this thing, alpha over s squared, plus alpha squared, times-- or, you know, I could just say times-- 1 over s squared, plus 2s.
This thing-- let me rewrite it-- 1 over s squared plus 1 times s squared plus 4 should be able to be rewritten as two separate fractions, s squared plus 1 and s squared plus 4.
So we're going to write it as 1 minus e to the minus 2 pi s, all of that times-- I will do it in orange-- all of that times 1 over s squared plus 1 times s squared plus 4.
So this is equal to y plus-- I'm just adding this whole term to both sides of this equation-- plus a squared over s squared y is equal to-- so this term is now gone, so it's equal to this stuff.
I think you're going to see in a second why I'm writing this way-- minus 1/3 times 2 over s squared plus 4, and then plus 2/3 times 1 over s squared plus 1.
So it's s squared plus a squared, over s squared, y is equal to minus e to the minus st, times this whole thing, sine of at, minus 1 over s squared, cosine of at.
They give us that the Laplace transform of some function is equal to 2 times s minus 1 times e to the minus 2s, all of that over s squared minus 2s plus 2.
It's just 1 over s squared plus 1.
So we get 1 plus a squared, over s squared, times y.