# Tagged Questions

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### Laplace transform quick answer check :) using second shift theorem

I want to get $L((t-4)^2u(t-4))$ I say this is a second shift with $g(t)=(t^2-4t)$ and my friend says "NO you are wrong, you are dumb!!!!!! $g(t)$ is MOST CERTAINLY equal to $t^2$" Mine gives me ...
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### Laplace transform on a non-standard sort of problem

I don't know where a laplace comes into play here: $\ddot{a}+2a=0,a(0)=b_1,\dot{a}(0)=b_2$ I am meant to solve the above using a Laplace transform, but I don't see how I would use it here? I ...
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### 'Deriving' the Laplace Transform from the $z$ Transform: Missing a $\Delta t$

Textbooks normally give the following 'derivation' (or justification, if you prefer) of the z-Transform from the Laplace Transform. Let $x(t)$ be a signal defined on $t\geq 0$, and write a discretized ...
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### Laplace transform of a differential equation

Given the Laplace transform \begin{align} \mathcal{L}\{g(r)\} = f(t) = \int_{0}^{\infty} e^{-tr} g(r) \ dr \end{align} can it be shown that the transform of the differential equation \begin{align} ...
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### Laplace transform of $L({1-e^{-t}\over t})$

I have to find the Laplace transform of $$\mathcal{L}\left[\dfrac{1-e^{-t}}t\right],$$ then this is equivalent to $$\mathcal{L}\left[\dfrac{1}t\right]-\mathcal{L}\left[\dfrac{e^{-t}}t\right]$$ But ...
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### Prove that the Laplace trasform is a Linear trasformation

Could you help me prove that the Laplace Trasform is a Linear trasformation? Thank you.
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### Laplace transform of $\sin(x)$

I am confused with Laplace transform of $\sin(\theta)$. For example, what is the LT of $A \sin(x(t))=Bx''(t)$ ($x$ is second order), $A,B$ are constants.
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### Laplace transform - frequency differentiation property (generalization)

Let $\mathcal{L(f(t);s)}$ be the Laplace transform of a function $f$. It is known that the Laplace transform of $\mathcal{L}{(t^nf(t);s)}$ is given as (frequency differentiation property) ...
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### Is that possible to solve the following differential equation by using laplace transform?

Is that possible to solve the following differential equation by using laplace transform? $$y''-t^2y'+y=e^{2t};\quad y(0)=1,\quad y'(0)=1$$ ?? I knew that if there is coefficient except $1$ with ...
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### Find the inverse Laplace transformation of $\frac{e^{-s}}{s+2}$

My question is: Find the function $f(t)$ that has the following Laplace transform $$F(s)=\dfrac{e^{-s}}{s+2}$$ Thanks . my try:I have find this Find the inverse Laplace transformation of ...
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### Laplace Transformation spring question

Here is the question: http://i.imgur.com/XAH2UnX.jpg I can't seem to get the answer. Are those values in the writing like 1N/m even relevant? Can someone give me some direction? Thanks!
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### Laplace Transform Involving Heaviside Step Function

I'm trying to find the Laplace transform of $7 e^{-3t} u(t-3)$, where $u$ is the heaviside step function. However, we've never really gone through what the Laplace transform of the heaviside step ...
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### Laplace Transform using t-shift

$$f(t)=\begin{cases}cos(πt), & 1\leq t < 4 \\ 0, &elsewhere \end{cases}$$ Okay, I attempted to write it in terms of step functions and I got $$f(t) = cos(πt)u(t-1)-cos(πt)u(t-4)$$ But ...
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### Using Convolution Theorem to find the Laplace transform

In previous questions I have used Laplace transform to find the inverse Laplace transform. I have worked through this work booklet ...
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### Find Laplace Transform of the function

$$f_T(t)=\begin{cases}2, & 0\leq t < T \\ 1, & t\geq T \end{cases}$$
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### I need to find a Laplace Transform but have problems

Using Laplace transform find: $e^{-10t}u(t)$. According to the Laplace table, that is equal to $1/s+10$, but how can I prove it?