To Päällikkö:
Oh sorry I forgot ln while putting the expression for t.
Thanks, however, for your explanation for ignoring the minus sign.
Another request: would you kindly discuss the motion of a heavy chain hung from a smooth pulley/peg/hook in general? I have doubts about the procedure I...
Oh I think you meeant to write
...=g*M/2a(-2a+2y)
Let me calculate:
y'' = (g/a).(y-a)
That gives general soln:
y-a = A.exp(kt) + B.exp(-kt), where k2 = g/a
Boundary values:
b = A + B ----------------> (1)
y' = k{ A.exp(kt) - B.exp(-kt)}
So,
0 = A - B ------------------>(2)...
OK, but it doesn't hint at the eqn of motion. Let the linear density be d. So, the net force on the chain is {(a+b) - (a-b)}d.g = 2bdg.
But how can I have the eqn of motion? It seems that there might be some A(b) such that A.b'' = 2bdg, where b'' = d2b/dt2; but what is A, then? Is A = (a+b)d...
Yes I thought of that case, too. But the problem is, I am not sure about the forces that would work at the end points - the tension of the chain may not remain equal at both sides' end points, and I am not sure how the tension varies. So I'd be able to immediately see the eqn of motion of the...
Would anyone kindly discuss the motion of a heavy chain ?
A typical problem I am stuck with is as follows:
A uniform chain of length 2a is hung over a smooth peg, with the lengths (a+b) and (a-b) of two sides. Motion is allowed to ensue - show that the time the chain would take to leave the...
Point set theory is simply topology. The point set theory of real numbers is the topology of the real numbers.
Point set theory has been much developed. Yet no one can say that no further research is needed - you may very well be interested in research in general topology.
Vector analysis is...
Please help:
A manufacturer of biscuits is considering three types of gift packs
containing three types of biscuits, Orange Cream (OC), Chocolate
Cream(CC) and Wafers (W). Market research study conducted recently
shows that three types of assortments A, B and C are in good demand...
Hmm.. each f_n is uniformly continuous, then if the seq {f_n} converges uniformly, the trick is done.
For the triangular waves become more little as n surges up, I think the convergence is uniform. But, can you dfevise a formal, maybe inductive, proof?
Can you please "formally" define your function? "if we infinitely repeat..." is not a formal term and I am not sure the ultimate function remains a continuous one.
Indeed, if Axiom of Choice is assumed, the set of all finite subsets of an infinite set \alpha has the same cardinality as \alpha.
This is seen in this way: Call the set of all finite subsets F(\alpha).
|F(\alpha)|=\displaystyle \sum_{n\in\mathbb N}|\alpha^n|\\
= \displaystyle...