Isn't the \lambda for the third harmonic \frac{2L}{3}?
If you use hookes law, don't we need to know the spring constant k before using this information to solve this problem?
Sorry to keep badgering you here, but I do not see how you get
\frac{1}{2}C^{-3/2}\int_{0}^{\infty}\sqrt{x} e^{-x}dx
The \sqrt{x} should be an x/C no? We let x = Cv², so that makes v² = x/C. The term you are substituting for there is v² not v. That would make the integral...
Oh ok, so you are saying that the original equation should be:
\int 4\pi\ (\frac{M}{2\pi RT})^{3/2} \cdot v^2 \cdot e^{\frac{-Mv^2}{2RT}} dv = 1
instead of:
\int 4\pi\ (\frac{M}{2\pi RT})^{3/2} \cdot v^2 \cdot e^{\frac{-Mv^2}{nRT}} dv = 1
?
Thanks for the reply, but I still seem to be a little lost. If I let C = \frac{M}{2RT} , that leaves me with 4 \pi \cdot ( \frac{C}{ \pi})^{3/2} \int \frac{x}{C} ... . I don't see how making the C = \frac{M}{2RT} helps me in the latter half of the integral because I have a n term in there...
Homework Statement
Given Maxwell's probability distribution function,
P(v) = 4\pi\ (\frac{M}{2\pi RT})^{3/2} \cdot v^2 \cdot e^{\frac{-Mv^2}{nRT}}
Where v = velocity, M = molar mass, R = Universal Gas Constant, n = # of mols, T = temperature, solve
\int P(v) dv =1 from 0 to...
Hi,
I have a question about the transfer of electrical charge from object to another. Basically, my professor stated that if you rub a rod with certain matierials, the rod will become charged. This is due to the convention that Ben Franklin came up with called the triboelectric series. So...
Homework Statement
A rod of length L carries a charge Q uniformly distributed along its length. The rod lies along the y-axis with one end at the origin. Find the potential as a function of position along the x-axis
Homework Equations
dV=\vec{E}\cdotp d\vec{l}
V=\frac{kq}{r}...
Homework Statement
Find the curvature of y = x³
Homework Equations
k(x) = \frac{f"(x)}{[1+(f'(x))²]^{3/2}
The Attempt at a Solution
k(x) = \frac{6x}{(1+9x^4)^{3/2}
I got the answer numerically, but I am looking for an explaination of the graph itself. I chose a relatively...
Homework Statement
a) Consider the initial value problem \frac{dA}{dt} = kA, A(0) = A_0 as the model for the decay of a radioactive substance. Show that in general the half-life T of the substance is T = -\frac{ln2}{k}
b) Show that the solution of the initial-value problem in part a) can...
Yes you did AKG, sorry about that. I just did not see how to factor them. I guess I am not very strong with my factoring and it was not very clear to me.
Thanks for the hint Daniel, that will help me out a lot.
Ok, going to go and work this out now!
I am asked to solve this DE with the initial condition of y(1) = 1.
(x+y)^2dx + (2xy + x^2-1)dy = 0
So, after working the problem out, I came to this as an answer:
F(x,y)=\frac{1}{3}x^3 + x^2y + xy^2-y
My question is what do I do with the initial condition. I assume that I am just...
\frac{\partial_P}{\partial_y}(2ysinxcosx-y+2y^2e^{(xy^2)}
I worked the first part no problem, but the second part I needed a little help from my calculator. This is what I got:
2sinxcosx-1+4ye^{(xy^2)}
My question is, why does the partial of 2y^2e^{(xy^2)} come out to 4ye^{(xy^2)}...
ok, so I tried it and I got 1+\frac{5(x-y+1)}{xy-2x+4y-8} which does not seem to help me out too much.
The form of both the numerator and the denominator do look a little suspicious. Is there a way to factor them like we can for a problem in the form ax^2 + bx + c?