Recent content by aracharya

Note however that not all solutions are valid equilibrium points. For example consider the case where the fixed points are distributed on a circle with equal angular spacings. Then if the springs are under tension, the centre of the circle is an equilibrium point. However if the springs are...

Consider the "floating point". Each spring yields a force with an x component , a y component, and a z component. If we sum all the x components, we get the net force in the x direction. Likewise for y & z. For the "floating point" to be in equilibrium, the net force in each direction (x,y,z)...

I am glad your professor didn't tell you the answer, because as a result I have learned something new from your post:) My approach was different. I was motivated by http://en.wikipedia.org/wiki/Partition_%28number_theory%29#Generating_function". In the below \mathcal{M}(n,d) is the...

I haven't read it yet but https://www.physicsforums.com/showthread.php?t=367945", is most certainly relevant to your question. Here is my attempt, which to be honest is a complete overkill since it resorts to a more advanced theorem!:), but it was pretty much the first thing that came into my...

@Bob S : what you have stated is true for http://en.wikipedia.org/wiki/Adiabatic_process" processes (i.e. processes where no heat is transfered). For a quasistatic process where the system is thermally interacting with the environment (i.e. heat transfer allowed & compression performed...

Yes you are correct. I was not trying to imply that speed was required for heating it up. Just to add, if the system is thermally interacting with the environment & is initially in equilibrium, then we can ensure that it remains arbitrarily close to equilibrium during compression by...

As stated by russ_watters, if you compress rapidly, the temperature will increase. This is a non-equilibrium process. However if the system thermally interacts with the environment [http://en.wikipedia.org/wiki/Canonical_ensemble" ], then once equilibration with the environment takes place, the...

Note that the operator method of elibj123 is one way of deriving the Euler-Maclaurin formula, as is shown in Chapter 25...

All I am doing is substituting f(n) = 1/\sqrt{n} into the Euler-Maclaurin formula. This time from Mathworld (since the formula is expanded in full), the http://mathworld.wolfram.com/Euler-MaclaurinIntegrationFormulas.html" formula can be written as : \sum_{k=1}^{n-1}f(k)=\int_0^n f(k)...

As stated in http://en.wikipedia.org/wiki/Bernoulli_numbers" if the first Bernoulli number is chosen according to the convention B_1 = -1/2 then the Euler–MacLaurin formula is : \sum\limits_{a\leq k<b}f(k)=\int_a^b f(x)\,dx \ + \sum\limits_{k=1}^m...

You can also use the first 5 terms of the http://planetmath.org/encyclopedia/EulerMaclaurinSummationFormula.html" (i.e. the integral, the terms involving the first derivative, and the terms involving the second derivative) to approximate the sum as follows : S_n = \sum_{i=1}^n...