When I say the second integral is symmetric, I guess what i mean is that t is approaching infinity on both sides. But for the first integral, you can interpret it as an integral from a to 0 plus an integral from 0 to b, with 'a' going to negative infinity while 'b' goes to infinity. In that...
Hmm. Can you explain to me this then?
http://www.wolframalpha.com/input/?i=integral+of+arctan%28x%29+from+negative+infinity+to+infinity
The limit (2nd integral) converges to zero when I test it on mathematica tho.
Also, what is the Cauchy Principal Value? That seems to be zero.
Thanks for the replies guys.
I thought about the question a bit more. I believe that the two integrals are not the same. The first one can be split into the integral from -Infty to 0 + the integral from 0 to +Infty. These two integrals are both divergent and so the sum is divergent (there is...
Homework Statement
Is $\intop_{-\infty}^{\infty}\arctan(x)\, dx$ convergent?
What about $\lim_{t\rightarrow\infty}\intop_{-t}^{t}\arctan(x)\, dx$?
Homework Equations
The Attempt at a Solution
I think the first integral may actually be divergent the way its written and the second one...
Mathematica would solve that sort of equation just fine. So would Maple and Matlab for that matter. www.wolframalpha.com would also suffice. As for solving it by hand, I dont see any clear way to do it without a whole lot of work.
Perhaps you need a more precise answer like 1.75. If the homework system you are using is something like UTexas, 3 decimals are needed as they only tolerate 2% error.
Ok. Let us begin with this question. You are given the frequency of the LP (and thus the period as well), and you are given the mass of the penny. As you have written above,
Frictional Force = co-eff * Normal and centripetal acceleration = v^2/r = 4Pi^2r*frequency^2. For the penny to stay on the...
Ahh. I see my mistake. My mistake was assuming that the Path Difference/ Wavelength = 0.5. A value of 0.5 for the P.D./wavelength is not the smallest path difference. From a bit of trial and error, you will see that 2.5 (i.e. n=2, n+0.5 = 2,5) creates the smallest path difference with an answer...
The work you did seems to be on the right track, but perhaps use of different notation will clear things up. Since one speaker is located at the origin (0, 0) and the other speaker is located at (0, 4), we do not need the co-ordinates of the Point P1-P2 but rather its distance:
Since the Path...
You will need to know about standing waves and possible wavelengths to produce standing waves.
Have you been taught the derivation of the formula Wavelength = 4L/(2n-1) where n is the nth harmonic?
(Usually this is Taught as 4L/n where n = 1, 3, 5.. etc.
As pgardn mentions above, a magnetic field interacts with a charged particle in quite a peculiar way. Similar to a ball being spun on a string, the magnetic field exerts a centripetal force to the component of the charge's velocity that is perpendicular to the field (whew. that sounded like a...
Ah but think about it. Say we're looking at one interval of a cosine curve (0 to 2pi). How many max points are there? How many points cross y = 0? The points that cross y = 0 are like the nodes (when you multiply the cosine curve by -1 they remain invariant) while the antinodes are the points...
For a wooden bar with anti-nodes on both sides, the formula for wavelength is:
Wavelength = 2L/n, where L is the length of the bar and n is the harmonics number.
For three antinodes and 2 nodes, the bar is in its second harmonic and so wavelength is:
2L/2 = L
Since Frequency*Wavelength =...
Hello clombard1973, let me start off by saying something that many people should have said to you upon registering at this forum:
Welcome to physicsforums.com.
As for your reply to my post, I admit it was a rather snide remark on my end. However, doubt is part of the scientific method and it...
I believe you would use four turns, as the flux is induced in the four turn coil by the 121 turn coil. You will need to know that:
Change in Flux = Change in Field * Cross sectional Area
Change in field = permeability of a vacuum x N x A x (I/t) / length
**Note that it is N and not N^2 as you...
I find the above post very difficult to swallow. I believe that the force of gravity on the mass must be included in the 25 N of breaking tension (of course I do not have "four advanced degrees in electrical engineering and a doctorate" as clombard1973 claims).
Thus, the breaking tension is...
When you have a large tank and a small leak, it can take forever for the tank to drain (this is because it has a large cross-sectional area on top so the height of the liquid only decreases a little when a lot of volume goes out). Alternatively, when you have a small tank and a large leak, the...
The mass of the spring do not need to be used as stretching with 55g stretches from the equilibrium state (the equilibrium state holes the 45g from the spring and system)
So what do I use for the initial velocity of the block on the ramp? It cant be v', can it? Also, the v' refers to the velocity of the system, but how do you determine the velocity of the ramp itself to the ground?
Homework Statement
A block of m mass slides along a frictionless horizontal surface with a speed of v m/s. After sliding a distance of d, the block makes a smooth transition to a frictionless ramp inclined at an angle of theta ° to the horizontal. The ramp is not fixed to the frictionless...