Laplace Transform

Laplace Transform of e^t sint | L{e^t sint}

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The Laplace transform of e^t sint is equal to 1/[(s-1)2+1]. Note that et sint is a product of an exponential function and a sine function. Here we learn how to find the Laplace of e^t sint. The Laplace Transform of et sint is denoted by L{et sint}. The Laplace transform formula of et sint is … Read more

Laplace transform of cosh(at) | L{cosh t}

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The Laplace transform of cosh(at) is s/(s2-a2). Here we focus on how to find the Laplace of cosh at, the hyperbolic cosine function. The Laplace transform of cosh at is denoted by L{cosh at} and its formula is given by L{cosh at} = s/(s2-a2). Find Laplace Transform of cosh(at) Answer: The Laplace transform of cosh … Read more

Find Laplace transform of sin2t sin3t

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The Laplace transform of sin2t sin3t is equal to 12s/(s2+1)(s2+25). Here we learn how to find the Laplace of sin2t sin3t. Note that sin2t sin3t is the product of two sine functions. The Laplace transform formula of sin2t sin3t is given below: L{sin2t sin 3t} = $\dfrac{12s}{(s^2+1)(s^2+25)}$. Laplace of sin2t sin3t Answer: The Laplace of … Read more

Find the Laplace transform of (1-e^t)/t

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The Laplace transform of (1-et)/t is equal to log[(s-1)/s]. In this post, we find Laplace of (1-et)/t. The Laplace transform formula of (1-et)/t is given by L{(1-et)/t} = log[(s-1)/s]. Laplace of (1-et)/t Answer: The Laplace transform of (1-et)/t is log[(s-1)/s]. Solution: Let us recall the division by t formula: L$\Big[ \dfrac{f(t)}{t} \Big]$ = $\int_s^\infty F(s) … Read more

Laplace transform of sinh(at): Formula, Proof

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The Laplace transform of Sinh(at) is a/(s2-a2). Note sinh at is the hyperbolic sine function, where t is real. In this post, we will learn how to find the Laplace of sinh(at). The Laplace transform formula of sinh at is given below: L{sinh at} = a/(s2-a2). Proof of Laplace Transform of sinh(at) The Laplace of … Read more

What is the Laplace transform of (1-cost)/t?

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The Laplace transform of (1-cost)/t is equal to 1/2 log[(s2+1)/s2]. Here we find Laplace of (1-cost)/t. The Laplace transform formula of (1-cost)/t is given by L{(1-cost)/t} = 1/2 log[(s2+1)/s2]. Find the Laplace transform of (1-cost)/t Answer: 1/2 log[(1+s2)/s2] is the Laplace transform of (1-cost)/t. Solution: Here we will use the following formula: L$\Big[ \dfrac{f(t)}{t} \Big]$ … Read more

Laplace Transform of sin^2t | Laplace of sin square t

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The Laplace transform of sin^2t is equal to 1/2s – s/(2s2+8). In this article, we will learn how to find the Laplace of sin square t. The formula of the Laplace of sin2t is given below: L{sin2t} = 1/2s – s/(2s2+8). Find the Laplace Transform of sin2t Answer: The Laplace transform of sin square t … Read more

Laplace Transform of cos2t/t

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The Laplace transform of cos2t/t is not defined. Here we will learn how to find the Laplace of cos2t/t. The Laplace transform formula of cos2t/t is given below. L{cos2t/t} = undefined. Find the Laplace Transform of cos2t/t Answer: The Laplace of cos2t/t does not exist. Proof: The following two formulas will be useful to find … Read more

Laplace Transform of sin2t/t

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The Laplace transform of sin2t/t is equal to tan-1(2/s). In this article, we will learn how to find the Laplace of sin2t/t. The Laplace transform formula of sin2t/t is given as follows: L{sin2t/t} = tan-1(2/s). To evaluate the Laplace trasform of sin2t divided by t, we will use the two formulas listed below: What is … Read more