Recent content by Stargazer19385

I just repeated the graphs, this time with the a column going from 3.1, 3.0, etc, to -1.6. Column B is sin(sin(a1)), and column c is sin(a1). I graphed it, and I got the same exact graph as the original above, but different scale. I just don't understand it. Sin(90 degrees) = 1. Sin(1) = ...

I seem to be making errors converting between radians and degrees. Maybe I should just do the x-axis in radians to start with, to keep it simple. I just graphed my above equation, and the result looked very high frequency. Not what I expected.

Hmmm... I don't believe that spreadsheet. At 90 degrees, sin(90) = 1, and sin(1) = a bit over zero. Yet it shows it at 0.82. The spreadsheet uses radians. I thought I corrected for them by using b1 = sin(sin(3.14*a1/180)). I now realize I should have done b1 = sin(180*(sin(3.14*a1/180))/3.14).

Sin(sin(z)) looks like sin(z) but with a more leveled off peak maxing at 0.82 instead of 1.0, at least for z under 180 degrees. Under 40 degrees, the two look extremely similar. Sin can probably replace sin(sin) in my calculations at lower values.

Your above link has a derivation I can follow, which shows that x(theta) and y(theta) are simple sine functions. I do not see a x(t), but it is believable that theta(t) is a sine function, so the second respondent's equations for x(t) and y(t) look very believable. That is for small theta, which...

Thank you for the responses! That is what I needed. When I woke up this morning, not having checked here again yet, I was going to tackle this with some algebra. I was going to assume that one of them, say x(t), being an oscillating function, was likely a sine function, and that knowing the...

This is for a personal engineering project. I need the parametric equations y(t) and x(t) for a very simple pendulum. Assume no friction, no forcing, no variation in gravity, a point mass, and the tether angle is significantly less than 30 degrees. It has been a while since I did differential...

It was a book, not an article. I searched through 30 pages on Amazon and could not find the book. Many solid biological materials follow standard materials equations. It is just many of the soft ones that don't follow it because their microscopic structure is better modeled by a string unwinding...

I read a book on the properties of biological materials. Their stress strain curves have a highly variable modulus of elasticity that is even unlike rubber. The author mentioned J curves vs S curves, resulting from the difference in microscopic structure. None of what you google about yield...

Is this balloon in the atmosphere or in a vacuum? The vast majority of the balloons resistance to expansion comes from atmospheric pressure. The thickness of the balloon skin can probably be estimated by assuming conservation of volume, though it really depends on the, I think, Poison's ratio...

I'm not using acrylic paint. I plan to buy a block of optical quality acrylic for making lenses. To possibly increase the optical quality, I want to melt it and remove any tiny bubbles or unevenness. This depends of course on how far standard optical quality acrylic already is from perfect, and...

The acrylic concrete floor sealer is different from what I'm doing. When a thick enough layer hardens on top first, bubbles from evaporating solvent can form. I did not know that concrete is very porous and breaths. That makes me reconsider making molds. As for the laser to fire at bubbles, I...

Question #2 got my interest. I've seen CRT screens that look dark grey when turned off. But when I turn the computer on, the screen actually turns black. How is that possible? Optical illusion? Or with the grey, and I getting light from inside the monitor, but that light is blocked when the...

Suppose I want to make a good acrylic lens, with very few bubbles. Could my eyes tell the difference between perfection and standard optical quality acrylic? Would getting it very hot and low viscosity, and then centrifuging it, be a good way to separate out the bubbles and inclusions? How do...

By parallel surface, I think you mean plano surface, such as the plano back side of an convex plano lens where the bent rays hit it at a non zero angle on the way out, which is more angle sensitive than the way in. Carving the back side to be spherical concave, with a radius of curvature such...