Recent content by refrigerator

I just saw the stickied thread about posting homework-type questions here... I hope this doesn't qualify as a homework-type question. Although it does involve debugging my thought process, it is also a conceptual question about why my reasoning is wrong. If this counts as a homework-type...

Referring to slides 3-4 (page 2) of this link: https://www.princeton.edu/~stengel/MAE331Lecture9.pdf The author states the relationship between body rates [p q r] and Euler angle rates [φ_dot θ_dot ψ_dot]. I want to verify this but have been failing miserably... My reasoning: 1) p, q, and r...

An aside: if angular momentum can be derived from linear momentum, then for example in 2D statics why can we get three independent equations using force balance in 2 directions and moment balance?

I was thinking of a couple basic mechanics problems lately. What if you have a rod sitting in space at rest, and you shoot a bullet at its center. Linear momentum is conserved, and the problem is quite trivial. Now what if the bullet hit the rod slightly off of the rod's CG? I think linear...

I see, thank you for clarifying. Your explanation helps me see where these equations come from. So if I understand correctly, the moment equation, shear equation, and EI(x)\frac{∂^4w}{∂x^4}=-μ\frac{∂^2w}{∂t^2}+... are all basically just different derivatives of the same equation? Indeed, I...

Sorry, I am still confused. So which equation is the actual Euler-Bernoulli beam equation? So this:EI(x)\frac{∂^4w}{∂x^4}=-μ\frac{∂^2w}{∂t^2}+Fδ(x-L) is derived from this: M=EI\frac{∂^2w}{∂x^2} Did I understand correctly? Or is EI(x)\frac{∂^4w}{∂x^4}=-μ\frac{∂^2w}{∂t^2}+Fδ(x-L) the...

OK, so it looks like I can integrate the Euler-Bernoulli equation twice to get moment? EI(x)\frac{∂^4w}{∂x^4}=-μ\frac{∂^2w}{∂t^2}+Fδ(x-L) Integrate once (using integration by parts, I guess): EI(x)\frac{∂^3w}{∂x^3}-∫\frac{∂^3w}{∂x^3}(\frac{∂}{∂x}EI(x))dx = -μ\frac{∂^2}{∂t^2}(∫wdx) +...

M=EI\frac{∂^2w}{∂x^2} 1. What exactly is this? Is it like a geometric constraint? This equation doesn't seem to depend explicitly on external loading or beam boundary conditions. 2. Can I derive this starting from the Euler-Bernoulli beam equation? I am dealing with a beam with...

Suppose we have a second-order system with the following transfer function: G(s)= \frac{1}{s^{2} + 2ζω_{n}s +ω_{n}^{2}} To figure out its resonant frequency, obtain its frequency response function and then maximize it with respect to ω. You get: ω_{peak} = ω_{n}\sqrt{1-2ζ^{2}} So it appears...

Thank you to everyone who responded; I think I understand now.

Thanks for your response. I suppose if I thought of P as "mg" (except at the tip, and not the center of mass of the bar), then potential energy would become: V= 1/2 K\dot{θ}2 + PLcos(θ) which would indeed get me the correct answer. I guess it's not clear to me why exactly you can...

Homework Statement I am having trouble understanding how to apply Lagrange's equation. I will present a simplified version of one of my homework problems. Imagine an inverted pendulum, consisting of a bar attached at a hinge at point A. At point A is a torsional spring with spring...

Hmm, I currently do not have access to any books, so an electronic resource would be preferable. But I will make sure to take a look at that book as soon as I get access to a library. Looks like it has some useful information. I am looking for error propagation. I would like to determine a fit...

I am doing a calculation involving taking three or more temperature measurements and then plotting them against another quantity (dependent). I get a relationship that is pretty linear, so I take the line of best fit to obtain an equation with a slope and an intercept. Now, my question is...

I'm collecting voltage data, and I need a resolution of at least .05mV, which I think I can provide over the range of voltages with my inexpensive A/D board. The problem is, the signal fluctuates maybe 1mV up and down, and so I get a noisy signal. I've tried running a low-pass filter through it...