# Terminal velocity

I recently read Ancillary Justice, the Hugo and Nebula award winning novel by Ann Leckie and enjoyed immensely, but it had one paragraph that brought me up short. The reason involves fluid mechanics, so it seemed like a good topic for a blog post. But first the book. Ancillary Justice has a good story, but…

# Energy dissipation in damped vibrations

In the previous post in this series (which was four months ago—time flies), we looked at the free vibrations of damped single-degree-of-freedom (SDOF) systems, systems that can be modeled as a spring-mass-dashpot like this: The position of the mass, [u], can be expressed as a function of time, [t], through the formula [u = A…

# Trajectory

A couple of weeks ago, I followed a link to this article by Alejandro Tauber that purported to calculate how far you’d be flung from an amusement park ride called the Booster Maxxx. The article had achieved some popularity through a link on Boing Boing from the usually reliable Maggie Koerth-Baker. Given that this is…

# 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…