I define ##\theta## to be the angle a rope makes relative to z and ##\phi## is the angle relative to x. The branch is in the xz plane. From conservation of energy I got
$$ \frac{r_A^2}{2} \left[\left(\frac{\partial\theta_A}{\partial t}\right)^2 + \left(\frac{\partial\phi_A}{\partial...
AB is the seat. AC and BD are the ropes. CD is the branch. I assume the system remains under tension. The initial kick could be positioning the swing away from the minimum energy position then releasing. Mass is centered on the swing seat with some non zero moment of inertia.
A swing is suspended from a non-horizontal tree branch. Points C and D are fixed in space. All 4 line segments in the diagram have constant distance. After some initial "kick" imparts energy to the system the only force acting externally on the system is gravity.
Is it possible to predict the...
It seems to me slope is computed as a ratio. I don't see how this explicitly requires zero. In modern calculus the rise and run both approach zero but zero itself is a no go for the denominator at least. I don't see why we can't keep the numerator and denominator largish but increasingly more...
What good is the additive identity in symbolic math? Is it actually necessary? Why cant our number system be based on multiplication rather than addition and use 1 as the identity to which transformations are made to get other numbers? I think I read somewhere that that would work under group...
Why do we have the number zero? What makes it important? Can we create math like system that don't use zero but are nonetheless useful. What limits or biases does having or not having zero create when we do science?
I have been looking at my old calculus textbook because to my dismay I seem to have forgotten most of the calculus I learned. I am given 3 cases of ##(f+g)(x) ##.
Case 1 both f and g are even:
I know ##f(x) = f(-x) ## and ##g(x)=g(-x) ## for the domain of the function. I can reason by...
universe is "fine tuned" for life
http://web.mit.edu/rog/www/papers/fine_tuning.pdf
There is some evidence that the universe is "fine tuned" for life. If the fundamental constants of the universe were a little bit different then we couldn't exist. Roger White considers this evidence of a...
If I know the percentage by weight of elements in a formula I can calculate the relative ratios of atoms in the formula no problem.
What I can't figure out is how to turn that ratio into an empirical formula.
To put it mathematically how do I turn a decimal number into a an approximate...
1. Homework Statement [/b]
Consider a double-paned window consisting of two panes of glass, each with a thickness of 0.500 cm and an area of separated by a layer of air with a thickness of 1.75 cm. The temperature on one side of the window is 0.00 °C; the temperature on the other side is 20.0...
Is that how the question is exactly worded? I think this is one those questions that tries to get you to discover something by thinking about it but from the way its worded I'm just not sure.