Search results

  1. P

    Pushing force with friction

    Simon, Thanks so much! :) Adrian
  2. P

    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...
  3. P

    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...
  4. P

    Laplace Transform

    Oh crap. The negative sign! Sorry it was late last night and somehow I thought he was saying \mathcal{L}\{y(t)\}\neq Y Sorry about that. He even says it's +4y not -4y. Geez :-(
  5. P

    Laplace Transform

    Pretty sure it is.
  6. P

    Laplace Transform

    Thanks! Duh!
  7. P

    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...
  8. P

    Inflection point conc up/down

    Thanks for correcting me. It was really late last night :-)
  9. P

    Inflection point conc up/down

    Yup. No problem. Feel free to ask. I'm struggling with math myself :-)
  10. P

    Inflection point conc up/down

    As you mentioned f''(x)=-6x-6=-6(x-1). So there is a root at x=1. Let's look at when f''(0) and when f''(2). f''(0)=-6(0)-6=-6 which means concave up. f''(2)=-6(2)-6=-12-6=-6 which means concave down.
  11. P

    Inflection point conc up/down

    Notice my f(x) is different from your problem. I'm making up a whole new problem. I was hoping you take take my example and figure out your problem.
  12. P

    Inflection point conc up/down

    Let's take the last part of your equation for an example. f(x)=-3x^{2}-4x-2 f'(x)=-6x-4 The root of the first derivative is when x=-2/3. So let's plug in -1 and 0 since it's to the left and right of the critical point. f'(-1)=-6(-1)-4=2 So from -\infty to -1 it is increasing. Now let's plug in...
  13. P

    Inflection point conc up/down

    Sorry latex fail :-P It's fixed now. If you need more examples, feel free to ask.
  14. P

    Inflection point conc up/down

    It is concave down when the second derivative is negative. It is concave up when the second derivative is positive. Let's say f(x)=x^{3}. f'(x)=3x^{2} f''(x)=6x First derivative tells you whether the function is increasing or decreasing. Second derivative tells you the concavity. If the...
  15. P

    LaTeX How I can use a vertical bar to represent evaluation in LaTeX

    I'm using lyx and I'm having difficulty trying to find the code for this vertical line. Any suggestions? I use the | but it's extremely small.
  16. P

    Inverse Fourier Transform

    Got it! Dang those minus signs :-P Thanks!
  17. P

    Inverse Fourier Transform

    I don't see where the sign is wrong. I broke it up the absolute value so it reads like follows: f(\omega)=\begin{cases} e^{\omega\alpha} & \mbox{if }\omega<0\\ e^{-\omega\alpha} & \mbox{if }\omega>0\end{cases}
  18. P

    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...
  19. P

    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...
Top