Posts tagged ‘mechanics’

Damped free vibrations

The second simplest vibrating system is composed of a spring, a mass, and a damper. We’ve seen the spring and the mass before, so let’s talk about the damper. The image typically used to represent a damper is meant to look like the cross-section of a hydraulic cylinder1 with a leaky piston, a device called…


Energy and gravity

At the end of the previous post on vibration, I said the next one would be on damped systems, but I’ve thought it would be best to discuss a couple of side topics before we move on: energy and gravity. The mechanical energy of our spring-mass system is composed of two parts: the kinetic energy…


Free, undamped vibrations

Let’s start with the simplest vibrating system, a spring and a mass: (You can ignore the free body diagram in the right half for the moment. We’ll return to it in a bit.) There are lots of oscillating systems that have the same behavior as the spring-mass system. The pendulum is an important historical example,…


Screwed up

I’m deeply disappointed in each and every one of you. Last night, in the post about jacking up a bed to remove the headboard, I said The jack’s leverage, meant to lift a car, was so great I could lift the bed by turning the screw with my fingers. and none of you took to…


Steel in Extremis

I saw Iron Man 3 with my family Saturday night. It was fun (Ben Kingsley was especially good), but there was a part that bothered me a bit. I tweeted about it later: Iron Man 3 was fun, but that water tower in Tennessee should’ve fallen long before its leg melted.— Dr. Drang (@drdrang) Sat…


Now we see the violence inherent in Hooke’s Law

This is the post where I explain how I avoided shooting my older son with the head of a screw. Two heads of screws, actually, but we’ll get into the details later. The underlying topic is strain energy, its potential1 for harm, and the respect it should be paid. As I said a few days…


Revisiting Castigliano with SciPy

On Friday, a colleague asked me if I had a quick solution for determining the spring stiffness of a tapered leaf spring. Yup. This may be the first time I’ve been able to use an old blog post directly for work. But as I read through the solution, I realized I’d done the numerical integration…


Programmers and physics

I’m sure it’s an age thing. Despite over 30 years of evidence to the contrary, I still think of programming as an adjunct to math and science, so I’m always shocked when I see things like this little writeup by Hannu Kankaanpää. It’s an explanation of how to write a program that tracks the motion…


Lego towers and the Menai Straits Bridge

You’ve probably seen this BBC News Magazine article on the maximum height of a tower of Lego bricks. I read it yesterday through a link from the indispensable Seth Brown (@DrBunsen), and was immediately reminded of this 1826 paper on suspension bridges by Davies Gilbert. That Gilbert paper is my white whale. I first saw…


Beams and potato chips

At Ryan Irelan’s request, @drdrang I really want to see a blog post about potato chips.  — Ryan Irelan (@ryanirelan) Sun Nov 18 2012 9:47 PM CST here’s a post about the structural design of potato chips by way of Euler-Bernoulli beam theory.1 Let’s start with a straight prismatic beam. We use the word “beam” to…