Question

The time period of a simple pendulum is directly related to the square root of its length. An 8 foot pendulum has a period of 3.2 seconds . find a period for a grandfather clock that has a pendulum length of 3 feet.

Answer 1

$T_1=k \sqrt{8}$

$T_2=k \sqrt{3}$

$\frac{T_2}{T_1} = \frac{T_2}{3.2} = \frac{ \sqrt{3} }{ \sqrt{8} }$

Then:

$T_2=3.2 \sqrt{ \frac{3}{8} } =1.96$ secs