Homework Statement
There is a cylinder of conducting ionized gas that occupies rho < a. For the given B, show that a suitable A can be found with only one non-zero component, Aphi, find Aphi which is also continuous at rho=a. (Part A was solving for a few relavant things)
Homework Equations...
Homework Statement
Consider a bead sliding without friction on a circular hoop of wire rotating at constant \Omega, where \phi is the angle between the bottom of the hoop and the bead. Find the equation of motion of the bead.
\hat{\Omega}=\hat{z}
Homework Equations...
Question:
A Particle of mass m can slide freely along a straight wire placed in the x-y plane whose perpendicular distance to the origin O is h. Denote the projection of O on the wire by on the wire by C. The line OC rotates around the origin (in the x-y plane) at a constant angular velocity...
I know, not directly, but I'm looking for a relation that's something along the lines of E=\hbar\omega but I don't know of any.
Essentially, I'm going from a unitless/normalized frequency of 2 to 80 mevs using \omega=2\sqrt{K_i/M} where K_i is 10.6 eV/\AA^2 and M is the mass of silicon. I...
I'm writing a program to demonstrate the chaotic system of two balls in one dimension with gravity. Before I can get even remotely close to that, however, it would help if my energy was conserved, so I'm apparently doing something wrong but I can't figure it out.
There is no damping forces...
ugh, of course. (second method)
So trivial once you're reminded ^^
Thanks.
So from
\frac{dy}{dt}=\frac{e^{\frac{t}{a}}}{a} + \frac{y}{b}
we get
\frac{d(ye^\frac{t}{b})}{dt}=\frac{e^{\frac{t}{a}-\frac{t}{b}}}{a}
which gives the solution (assuming at t=0 y=0)
y = \frac{-abe^{\frac{t}{a} -...
\frac{dy}{dt}=t-y
Where y is a function of t.
Just... not quite sure how to do it.
Also, would the method change if it was e^-t instead of t? I don't see why it would, but if it does, that's what I'm actually working with.
Thanks for any help.
Problem:
Let \vec{x} and \vec{y} be vectors in Rn and define
p = \frac{x^Ty}{y^Ty}y
and
z = x - p
(a) Show that \vec{p}\bot\vec{z}. Thus \vec{p} is the vector projection of x onto y; that is \vec{x} = \vec{p} + \vec{z}, where \vec{p} and \vec{z} are orthogonal components of \vec{x}...
I'm not sure I understand what you mean.
I know the 1 year is in proper time of the spaceship, but I thought that would make it the unprimed frame and the Earth the primed frame. is that backwards?
Homework Statement
Plans are made to send a spacecraft from Earth to a nearby start 10 light years away. The system support will last one year and one day. The trip is one way trip.
a) What speed must the craft travel to arrive at the star with battery power for one day to make the...
Working with the binomial expansion,
if I want to evaluate (1-x)^{-1/2} I thought I would get something like...
(\stackrel{-1/2}{0})1-(\stackrel{-1/2}{1})x+(\stackrel{-1/2}{2})x^2...
I thought that was right, but (\stackrel{-1/2}{1}) and the likes can't be evaluated, can they?
Hope my...
I was under the impression that the binomial theorem worked only when n is a natural number.. so I rose the power of each side by 4, then 6 to see what would happen... (their negatives, actually)
my result (if m is the number I'm raising the eqn to) is essentially:
\gamma=(1-m/2*v^2/c^2)^{-m}