Pendulum

Calculate the pendulum's length 2 cm lower in the lowest position than in the highest position. The circular arc length to be described when moving is 20cm.

Correct answer:

l =  25 cm

Step-by-step explanation:

$$\begin{gathered} x=2\text{cm} \\ o=20\text{cm} \\ {o}_2=o/2=20/2=10\text{cm} \\ {t}^2=o_2^2-x^2 \\ t=\sqrt{o_2^2-x^2}=\sqrt{10^2-2^2}=4\sqrt{6}\text{cm}\doteq 9.798\text{cm} \\ {l}^2=(l-x{)}^2+t^2 \\ {l}^2=l^2-2l_x+x^2+t^2 \\ 2l_x=x^2+t^2 \\ l=(x^2+t^2)/(2\cdot x)=(2^2+9.798^2)/(2\cdot 2)=25\text{cm} \end{gathered}$$

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