Worked exercise — Seconds pendulum

Problem

A seconds pendulum is calibrated so that the period is $T = 2$ s (one second to go, one second to return). How long must it be?

Solution

Set-up. From the simple pendulum period $T = 2\pi\sqrt{\ell/g}$ we obtain the length: $\ell = \frac{g T^2}{4\pi^2}$

Numerical substitution ($g = 9{,}81$ m/s$^2$, $T = 2$ s): $\ell = \frac{9{,}81\cdot 4}{4\pi^2} \approx \ev{0{,}994 \ \text{m}}$

About a metre: this is the traditional length of pendulums in early nineteenth-century mantel clocks.

Links

Topics: Oscillazioni e moto armonico Concepts: Pendolo semplice · Periodo e frequenza Objects: Pendolo semplice