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    Pushing force with friction

    I just want to check to see if I did the problem correctly. A person pushes a 2.0 kg box across a flat, horizontal surface with a force of 5.0 N for 4.0 m. Determine the acceleration of a box if the friction coefficient is 0.2. Determine the acceleration of the box if the friction coefficient...
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    Fredholm's Alternative

    Homework Statement This is not a book problem but rather just a question about how the book got here. \frac{d^2u}{dx^2}+u=e^{x} \quad \mbox{with} \quad u(0)=0 \quad \mbox{and} \quad u(\pi)=0 \Rightarrow \frac{d^2\phi}{dx^2}=-\lambda \phi \quad \mbox{with} \quad \phi(0)=0 \quad \mbox{and} \quad...
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    Laplace Transform

    [Solved] Laplace Transform Homework Statement \frac{d^{2}y}{dt^{2}}+4y=sin(t),\quad y(0)=0,\quad\frac{dy}{dt}(0)=0 Homework Equations Laplace transform is defined as: \mathcal{L}\{f(t)\} = \int_{-\infty}^{\infty}f(t)e^{st}dt The Attempt at a Solution...
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    Inverse Fourier Transform

    [Solved] Inverse Fourier Transform Homework Statement If F(\omega)=e^{-|\omega|\alpha}\,(\alpha>0), determine the inverse Fourier transform of F(\omega). The answer is \frac{2\alpha}{x^{2}+\alpha^{2}} Homework Equations Inverse Fourier Transform is defined as...
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    Solving Diffusion equation with Convection

    The problem is as follows: \frac{\partial u}{\partial t}=k\frac{\partial^{2}u}{\partial x^{2}}+c\frac{\partial u}{\partial x}, -\infty<x<\infty u(x,0)=f(x) Fourier Transform is defined as: F(\omega)=\frac{1}{2\pi}\int_{-\infty}^{\infty}f(x)e^{i\omega x}dx So, I took the Fourier...