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L{cos(at)} = s/(s2 + a2)

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14y ago

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What is Laplace transform?

A Laplace transform is a mathematical operator that is used to solve differential equations. This operator is also used to transform waveform functions from the time domain to the frequency domain and can simplify the study of such functions. For continuous functions, f(t), the Laplace transform, F(s), is defined as the Integral from 0 to infinity of f(t)*e-stdt. When this definition is used it can be shown that the Laplace transform, Fn(s) of the nth derivative of a function, fn(t), is given by the following generic formula:Fn(s)=snF(s) - sn-1f0(0) - sn-2f1(0) - sn-3f2(0) - sn-4f3(0) - sn-5f4(0). . . . . - sn-nfn-1(0)Thus, by taking the Laplace transform of an entire differential equation you can eliminate the derivatives of functions with respect to t in the equation replacing them with a Laplace transform operator, and simple initial condition constants, fn(0), times a new variable s raised to some power. In this manner the differential equation is transformed into an algebraic equation with an F(s) term. After solving this new algebraic equation for F(s) you can take the inverse Laplace transform of the entire equation. Since the inverse Laplace transform of F(s) is f(t) you are left with the solution to the original differential equation.


What is the value of scalar product of two vectors A and B where value of vector A and B is not zero and vector product of two vectors A and B is not zero?

Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')


Why do cosine to the negative 1th power and cosine cancel out each other?

Cosine to the negative first power and cosine cancel each other out because cosine to the negative first power is one over cosine, and one over anything times anything is just one.


What is Secany squared times cotangent times cosine?

Assuming that "secany" is meant to be secant, the answer is cosecant.


Why work is scalar but product of two vector?

The product of two vectors can be done in two different ways. The result of one way is another vector. The result of the other way is a scalar ... that's why that method is called the "scalar product". The way it's done is (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).


How do you find cosine direction?

look 3 times left then 7times up and you will be at mt etna


What does sine times cosine equal?

Sin(x) cos(x) = 1/2 of sin(2x)


How do you transform into a pixie?

You just say pixies ten times.


What is it when two vectors' dot product is one?

That fact alone doesn't tell you much about the original two vectors. It only says that (magnitude of vector-#1) times (magnitude of vector-#2) times (cosine of the angle between them) = 1. You still don't know the magnitude of either vector, or the angle between them.


What product is equal to 2 times 3 times 3?

Product is 18.


What is the product for 3 times 9?

The product for 3 times 9 is 27. Product is the answer you get when you multiply numbers together.


What is the product for 4 times 8?

The product for 4 times 8 is 32. The product is the answer you get when you multiply numbers together.