Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2024 / Paper 3 / 7 / c

The displayed signal is a square wave with levels $+1\mathrm{V}$ and $-1\mathrm{V}$, each lasting two seconds. On a representative period it is positive for $0<t<2\mathrm{s}$ and negative for $2<t<4\mathrm{s}$.

The positive and negative contributions to the integral cancel. Hence the mean is $0\mathrm{V}$.

The waveform repeats after one positive and one negative interval, so its fundamental period is $T=4\mathrm{s}$. A two-second shift reverses its sign and is not a period.

The ordinary frequency is $\nu =1/T=0.25\mathrm{Hz}$, or one quarter of a cycle per second.

The angular frequency is $\omega =2\pi /T=\pi /2\mathrm{rad}{\mathrm{s}}^{-1}$. This is distinct from the ordinary frequency in cycles per second.

The amplitude relative to the zero mean is $1\mathrm{V}$. The peak-to-peak excursion is $2\mathrm{V}$.