Math

The catenary curve with a sliding end

We dive into calculus of variations to calculate the shape of a rope fixed in one end and free to slide on the other.

Integral of the month: \( \int dx \frac{\sin x}{x} \)

Three different ways of evaluating this lovely integral!

HDD average seek time

We compute the average seek time on an hard disk drive. This will involve a bit of math related to functions of random variables.

Integral of the month: \( \int \frac{ dx}{x^n+ 1} \)

Branch cuts are your friends. You can have fun with them!

Integral of the month: \( \int \frac{x^\alpha dx}{x^2- 2 \beta x + 1} \)

An integral with branch cut.

The math of low pass filtered PWM

This is a deep dive into the math of low pass filter with driven by a square wave.

Forced & damped Harmonic Oscillator

Mass-spring system with dumping and driving forces. A full solution is presented with interactive plots.