Laplace Transform

Laplace Transform of sint/t | Laplace of sin(at)/t

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The Laplace transform of sint/t is equal to tan-1(1/s), that is, L{sint/t} = tan-1(1/s). The formulas for the Laplace of sint/t and the Laplace of sin(at)/t are given as follows: $\boxed{\mathcal{L}\left\{\dfrac{\sin t}{t} \right\}=\tan^{-1}\left(\dfrac{1}{s} \right)}$ and $\boxed{\mathcal{L}\left\{\dfrac{\sin at}{t} \right\}=\tan^{-1}\left(\dfrac{a}{s} \right)}$ Lets learn how to find Laplace of sin(t)/t. Laplace of sint/t Question: What is the Laplace … Read more

Find Laplace Transform of e^4t | Laplace of e^-4t

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The Laplace transform of e^4t is equal to 1/(s-4) and the Laplace of e^-4t is equal to 1/(s+4). This is because, we know that the Laplace of eat is 1/(s-a). The Laplace transform formulae for the functions e4t and e-4t are given in the table below. Function f(t) L{ f(t) } e4t L{e4t} = $\dfrac{1}{s-4}$ … Read more

Find Laplace Transform of e^3t | Laplace of e^-3t

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The Laplace transform of e^3t is equal to 1/(s-3) and the Laplace of e^-3t is equal to 1/(s+3). This is because, we know that the Laplace of eat is 1/(s-a). The Laplace transform formula for the functions e3t and e-3t are given as follows. Laplace of e3t We will find the Laplace transform of e3t … Read more

Laplace Transform of e^2t | Laplace of e^-2t

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The Laplace transform of e^2t is equal to 1/(s-2) and the Laplace of e^-2t is equal to 1/(s+2). More generally, the Laplace of eat is 1/(s-a). The Laplace formula for the functions e2t and e-2t are given below: Laplace of e2t By definition, the Laplace of f(t) is given by the integral L{f(t)} = $\int_0^\infty$ … Read more

Laplace Transform of sin2t | Laplace of cos2t

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The Laplace transform of sin2t is equal to L{sin2t} = 2/(s2+4) and the Laplace of cos2t is L{cos2t} = s/(s2+4). Because, the Laplace of sinat is a/(s2+a2) and the Laplace of cosat is s/(s2+a2). In this post, we will find the Laplace transform of sin2t and cos2t. Laplace of sin2t and cos2t To find the … Read more

Laplace transform of delta function | L{δ(t)}

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The Laplace transform of delta function is equal to L{δ(t)} = 1. Here we find the Laplace of Dirac delta function, that is, unit impulse function. The Dirac delta function is also known as the unit impulse function. Its Laplace transform formula is given by L{δ(t)} = 1. Laplace Transform of Dirac Delta Function Recall … Read more

Laplace transform of unit step function | L{u(t)}

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The Laplace transform of unit step function is equal to 1/s. The unit step function, denoted by, u(t), is defined as follows: $u(t) = \begin{cases} 0, & \text{if } t<0 \\ 1, & \text{if } t \geq 0. \end{cases}$ The Laplace transform of u(t), unit step function, is given by L{u(t)} = $\dfrac{1}{s}$. Laplace transform … Read more

Laplace transform of e^t | Laplace of e^t

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The Laplace transform of e^t is equal to L{et} = 1/(s-1) whenever s>1. Here we find the Laplace of et by the definition of Laplace transforms. The formula of the Laplace of et is given by L{et} = $\dfrac{1}{s-1}$. Find the Laplace Transform of et By definition of Laplace transforms, the Laplace transform of a … Read more

Laplace Transform of t | Laplace of t

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The Laplace transform of t is equal to L{t} = 1/s2. Here we will find the Laplace of t by the definition of Laplace transforms. The formula of the Laplace of t is given as follows: L{t} = $\dfrac{1}{s^2}$. Find Laplace Transform of t Recall, the definition of the Laplace transform. According to this, the … Read more