Recent content by PhysicsMark

1. Simple Integral

Nevermind. I guess the second part of the problem is incorrect. Mathematica has arrived at the same conclusion as this also. Thanks for all the help.
2. Simple Integral

Thank you Dick and Jgens. \int{x^3}\sqrt{1+x^2}dx Let u=1+x^2\rightarrowdu=2xdx \int{x^3}\sqrt{1+x^2}dx=\frac{1}{2}\int(u-1)\sqrt{u}du \frac{1}{2}\int(u-1)\sqrt{u}du=\frac{1}{2}(\int{u^{\frac{3}{2}}}du-\int{u^{\frac{1}{2}}du) \int{u^{\frac{3}{2}}}du=\frac{2}{5}u^{\frac{5}{2}}...
3. Simple Integral

Homework Statement Hello. I have a simple integral here that has been stumping me for the last 30 minutes. It appears that my basic integration skills have gotten very rusty. Homework Equations \int{x^3}\sqrt{1+x^2}dx The Attempt at a Solution I am pretty sure a simple...
4. Finding position and velocity from Force (analytic mechanics)

Homework Statement A body of mass "m" is repelled from the origin by a force F(x). The body is at rest at x_0, a distance from the origin, at t=0. Find v(x) and x(t). Homework Equations F(x)=\frac{k}{x^3} \ddot{x}=\frac{d\dot{x}}{dt}=\frac{dx}{dt}\frac{d\dot{x}}{dx}=v\frac{dv}{dx}...
5. How fast is the distance changing? (FODE, I think)

Thanks. This makes sense to me also. I would like to point out something about this problem. I am not sure how relevant this is because the "correct" answer could have come from anywhere. I found this problem on another forum and could not solve it. The original poster came up with the same...
6. How fast is the distance changing? (FODE, I think)

Hmm, ok. Using your suggestions here is what I did: I re-wrote my equations (Thanks, organization is crucial) as: C(t)=\sqrt{(50t)^2+(27t)^2} I then simplified as follows: C(t)=\sqrt{t^2(50^2+27^2)} ...then: C(t)=\sqrt{t^2(3229)} ...and finally: C(t)=t{\sqrt{3229}}...
7. How fast is the distance changing? (FODE, I think)

Sorry about the abbreviation. In my DiffEq book, they use FODE to mean First Order ordinary Differential Equation. This problem does not come from my DiffEq book, but it did remind me of a similar problem in that book that also stumped me. Thank you for the hint. As always your posts...
8. How fast is the distance changing? (FODE, I think)

Homework Statement 2 cars start from the same point. Car A travels a constant 50 mph due west. Car B travels a constant 27 mph due south. After 3 hours, how fast is the distance changing between them? Homework Equations The Attempt at a Solution I saw this problem online...
9. Fit P(w) to determine Q,w, and R (Series RLC AC circuit)

Homework Statement Fit P(w) to determine Q, and w_0, and R. You should put in Vrms as a known constant. Homework Equations P(\omega)={\frac{V_{rms}^{2}}{R(1+Q^2(\frac{\omega}{\omega_0}-\frac{\omega_0}{\omega})^2)} Q=\frac{\omega_0}{\Delta\omega} R=R_load+r The Attempt at a...
10. Laplace Eq with Dirichlet boundary conditions in 2D (solution check)

Ahh, I see. Thanks again.
11. Laplace Eq with Dirichlet boundary conditions in 2D (solution check)

First, I forgot to thank you for taking the time to reply. Thank you. Gosh, I see. Sorry about the earlier post. I was thinking of only including the even numbers for some reason. Would you say that what you have posted above is "as good as it gets"? I was concerned about how I...
12. Laplace Eq with Dirichlet boundary conditions in 2D (solution check)

Are you suggesting an index change? As in swapping out all n's to the right of sigma with m, where m = 2n? Or changing the n's to n(n+1)?
13. Laplace Eq with Dirichlet boundary conditions in 2D (solution check)

Homework Statement The steady state temperature distribution, T(x,y), in a flat metal sheet obeys the partial differential equation: \frac{\partial^2{T}}{\partial{x}^2}+{\frac{\partial^2{T}}{\partial{y}^2}}=0 Separate the variables and find T everywhere on a square flat plate of sides S with...
14. How to check Fourier series solution (complex)

Thanks a lot! That is also the answer I got. I realized why maple wouldn't plot it, it was because I did not account for the "n" in the denominator. No wonder Maple was blabbering about a singularity.
15. How to check Fourier series solution (complex)

Thanks for the clarification, Vela. I spoke with my professor today, and he also said the original integral should be correct. He went on to say that I should be able to plot it in Maple. So, I guess that means I need some more practice in Maple (That should be no surprise to...