Recent content by bishy

Homework Statement question 1: Define ~ on Z by a ~ b if and only if 3a + b is multiple of 4. question 2: Let A = {1,2,3,4,5,6} and let S = P(A) (the power set of A). For a,b \in S define a ~ b if a and b have the same number of elements. Prove that ~ defines an equivalence...

That's what I thought as well when I first realized that little difference within the DE books I am basing the sets on. Considering that they we're using this method to get something backed by primary source papers I stopped trying to pass it off as a typo within my books. Apparently with the...

I'm a little confused with ODEs. After two weeks of trying to figure out Frobenius I have finally realized that there seems to be two different power set used by all of my three books for the y substitution but I am unsure when to use either one. Here are the two sets that I'm talking about...

Homework Statement A 32 pound weight stretches 2 feet. Determine the amplitude and period of motion if the weight is released 1 foot above the equilibrium position with an initial velocity of 2 ft/s upward. How many complete vibrations will the weight have completed at the end of 4 pi seconds...

Homework Statement 2y\prime\prime +2y\prime + y = 4 \sqrt{x}The Attempt at a Solution charecteristic equation: x^2+x+\frac{1}{2} roots: \frac{1}{2}\pm\frac{1}{2}i homogenous solution: a \sin{\frac{1}{2}x} + b \cos{\frac{1}{2}x} Wronskian...

ah ok. that's what I thought, I just wasn't sure. As for it not being a solution, I made it up and never bothered checking it. It's not a big a deal, most of the work I have done is confirmed with this.

I'm making an assumption while trying to solve DEs by reduction of order. I've got a short form equation that I can use to reduce it if and only if I can place the DE into standard form. The standard form with generic notation would be y"+ P(x)y' +G(x)y = 0 where P(x) and G(x) are continuous and...

Homework Statement An LC circuit starts at t=0 with its 2000 microF capacitor at its peak voltage of 14V. At t=35 ms the voltage has dropped to 8.5 V. a) What will be the peak current? b) At what time will the peak current occur? c) What must be the value of the inductor in the circuit?The...

Hows about this: By Lenz's law I expect that the penny will do work against the magnet. Since there is no change in potential energy this change has to be through kinetic energy. Since there is also no change in the mass of the penny, it must be velocity that is expected to change. This change...

Homework Statement A copper penny falls on a path that takes it between the poles of a magnet. Does it hit the ground going faster, slower, or at the same speed. The Attempt at a Solution Clearly the penny undergoes a change in magnetic flux. Since it receives a change in magnetic flux...

Thanks man. Solved it with your advice.

Can you explain why? I don't think that's right. Heres why. A solid sphere has a point of symmetry where the distance from this point gives you a charge density called r. In the question it states that the charge is uniform so I expect the electric field at a distance r within a sphere to be Q...

Homework Statement A solid sphere contains a uniform volume charge density (charge Q, radius R). (a) Use Gauss’s law to find the electric field inside the sphere. (b) Integrate E^2 over spherical shells over the volumes inside and outside the sphere. (c) What fraction of the total electrostatic...