Question

A clock pendulum has a period of 2.00s. A simple pendulum setup in front of it gains on the clock so

      that the two vibrate in phase at intervals of 22.0s. Calculate:

      (a.) the period of the simple pendulum

      (b.) the fractional change in length of the simple pendulum necessary for the two periods to be

      equal. 

Answer 1

Answer

A clock pendulum has a time period of $T_1=$ 2.00s

the period of the simple pendulum

$T_2=\frac{22}{2}=11sec.$

Now

the fractional change in length of the simple pendulum necessary for the two periods to be equal. 

$T=2\pi\sqrt{ \frac{l}{g}}$

Both periods are equal then

$T_1=T_2$

$2\pi\sqrt{ \frac{l_1}{g}}=2\pi\sqrt{ \frac{l_2}{g}}$

So fractional change in length

$\frac{l_2}{l_1}=(\frac{T_2}{T_1}) ^2=(\frac{11}{2}) ^2=30.25$