Recent content by No Name Required

Im stuck on this question :( The Hermite polynomials can be defined through \displaystyle{F(x,h) = \sum^{\infty}_{n = 0} \frac{h^n}{n!}H_n(x)} Prove that the H_n satisfy the hermite equation \displaystyle{H''_n(x) - 2xH'_n(x) + 2nH_n(x) = 0} Using...

bump... any ideas anyone?

Presume the Earth is spherical, homogeneous and of radius R. What should be the shape of a tunnel connecting two points on the surface in order to minimize the time it takes for a particle to travel between the two points. I have had a go at doing it in both polar and cartesian co-ordinates...

Thankyou very much for your time and thoughts. I have solved the problem in polar co ordinates and if anyone is particularly interested i will write it up for them. I will check back tomorrow.

I have this question, Express the length of a given curve r = r(\theta) in radial co-ordinates. Using the Variational principle derive the shortest path between two points is a line. Ive drawn a picture with two angles (measured from the x-axis) \theta_1 and \theta_2 so that r(\theta_1) =...

Centripetal forces? But if that is the case, why does it say find the force acting on the two VERTICES. That confuses me... Or is vertices correct? If so then the problem is basicall one of finding the distance of each particle from axis of rotation yea?

I have this question I am having trouble with. A massless rectangular parallelepiped with sides a, a and \sqrt{a} has equal masses attached to its vertices. It is rotating around its major diagonal with a constant velocity \Omega. Find the forces acting on the two vertices on the axis of...

wow! its amazing how tricky a simple enough looking question can get! It seems as if the answer posted by several of you is correct by a majority vote. I have learned a lot from this thread. Thankyou. I will be getting the solution to this next week. I will post what my lecturer has to say about...

Thanks everyone for your help! I've been sketching various stages in its falling and am carrying out several calculations. But then I had to sleep. I am true in also thinking that mechanical energy is conserved yes?

A thin uniform stick of mass m with its bottom end resting on a frictionless table is released from rest at an angle A to the vertical. Find the force exerted by the table on the stick at the moment of release. Express your answer in terms of m, g and A. Ive been reliably informed (from the...

Ah rite thankyou! :smile: I understand what you mean about the inequality bit. Also, i feel that the insertion of x = 0 is a valid one as it can be shown that the maximum acceleration to keep the particle on the plane occurs at the crests of the curve. So if it stays on the plane there...

Ok, Ive done this... \frac{dy}{dt} = -gt and \frac{dx}{dt} = v (is this right?) so \frac{dy}{dx} = -\frac{gt}{v} and \frac{d^2y}{dx^2} = -\frac{g}{v} \frac{dt}{dx} \frac{d^2y}{dx^2} = -\frac{g}{v^2} And \frac{d^2h}{dx^2} = -dk^2\cos(kx) This is where i get...

OK, I think i understand you. Would you be able to show me how you reached the answer you got in your first post please?

Hello! Thankyou very much Im a little confused with your idea. Are you saying that the velocity of the particle (which is tangent to the curve), must be less than \frac{dh}{dx}? Thankyou again.

Im having a little trouble starting this question Consider a particle moving without friction on a rippled surface. Gravity acts in the negative h direction. The elevation h(x) of the surface is given by h(x) = d\cos(kx). If the particle starts at x = 0 with a speed v in the x direction, for...