Length of Pendulum Increading by Factor of 9 Increaeses Period By 1 Second - Find Length and Period
\[t\]
to \[t+1\]
. What is \[T\]
and what is the length of the pendulum?The period of a pendulum is given by
\[T= 2 \pi \sqrt{ \frac{l}{g}}\]
.Originally
\[t= 2 \pi \sqrt{ \frac{L}{g}}\]
, and then \[t+1= 2 \pi \sqrt{ \frac{9L}{g}}\]
.Dividing the second equation by the first gives
\[\frac{t+1}{t}= \sqrt{9}=3\]
.Then
\[t+1=3t \rightarrow 1=2t \rightarrow t=0.5\]
.Then
\[T= 2 \pi \sqrt{\frac{l}{g}} \rightarrow l = \frac{gT^2}{4 \pi^2} =\frac{9.8 \times 0.5^2}{39.47}=0.062\]
m to 3 decimal places. 
