Problem — Clock pendulum

Problem

A pendulum clock beats the second (one beat per second, so half a period per beat). How long is the pendulum? Use $g = 9{,}81\;\text{m/s}^2$.

Solution

One beat corresponds to half a period (from the dead point on one side to the dead point on the other), so $\frac{T}{2} = 1\;\text{s} \quad\Rightarrow\quad T = 2\;\text{s}$ From the pendulum formula $T = 2\pi\sqrt{L/g}$ I obtain the length: $L = \frac{gT^2}{4\pi^2} = \frac{9{,}81 \cdot 2^2}{4\pi^2} = \frac{39{,}24}{39{,}48}$ $\ev{L \approx 0{,}994\;\text{m}}$ About a metre: this is the classic “seconds pendulum”.

Links

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