Recent content by KDawgAtsu

\displaystyle g'(x)=\sum_{n=1}^{\infty}2n(x^{2n-1})=\sum_{n=0}^{\infty}2(n+1)x(x^{2n})\,,\text{ or equivalently }\sum_{n=1}^{\infty}\frac{2n}{x}(x^2)^n Where did the x in front of the x^2n come from? I know you just shifted n=1 to n = 0, but I can't see where the x comes from?

Homework Statement Fin the Taylor series about x = 0 for: f(x) = 1 / (1-x2)2 Homework Equations g(x) = 1 / (1-x2) The Attempt at a Solution Differentiating g(x), the series representation of g'(x) is Ʃn(x2)n-1 Since f(x) = g'(x)/2x f(x) = Ʃ(n/2)x2n-1 I'm pretty sure that's right...

I don't need a solution to this problem, I just need some help understanding a part of it. Homework Statement The figure below shows a small mass, m, moving at an initial speed, v0 , colliding with a stick with length, L, and mass, M. Both the mass and the stick lie on top of a table. The...

Well there are no numbers involved in this FRQ, just variables. But yes, I can find k using the stopwatch and timing a period, then use T = 2\pi\sqrt{}m/k

Well the units work out, and I don't see why it wouldn't work out conceptually. Thank you for your help!

Hm, would it work if I simply measured the length of the spring of when the object is submerged and of when it is not, and find the difference in the forces, which would be the buoyant force?

The force of the spring is -kx, so by measuring the change in the x and using that equation, I would get the buoyant force? And with that, I would be able to use F=pvg, to solve for p. Am I correct?

Will the spring extend to its maximum length, since there is no more buoyant force pushing it up any more?

Homework Statement In the laboratory, you are given a cylindrical beaker containing a fluid and you are asked to determine the density \rho of the fluid. You are to use a spring of negligible mass and unknown spring constant k attached to a stand. An irregularly shaped object of known mass m...

Thank you all for the help, I think I understand this now.

By total velocity, I mean the final velocity of the marble in both the x and the y when it reaches the bottom of the ramp. The equation you are referring to would be x=0.5at2, correct? So 2.26=(0.5)a(3.12)2 2.26=4.87a a=0.464 m/s2 So I still end up with the same acceleration. The...

Homework Statement This was actually a lab for class today. Basically, a marble rolls down a 2.26m slope, in 3.12s. Find the angle of the slope. Assume there is no friction.Homework Equations v=d/t a=v t a=g sin (theta)The Attempt at a Solution v=2.26/3.12 = 0.724m/s since that is Avg. V...