Answer
a) .0099 meters
b) 6.2 meters
c) 3575 meters
Work Step by Step
We simplify the equation for the period of the pendulum so that length is isolated on one side of the equation:
$L = \frac{T^2g}{4\pi^2}$
We plug in each of the values to find:
a) $L = \frac{(200\times10^-3)^2(9.81)}{4\pi^2}=\fbox{.0099 meters}$
b) $L = \frac{(5)^2(9.81)}{4\pi^2}=\fbox{6.2 meters}$
c) $L = \frac{(120)^2(9.81)}{4\pi^2}=\fbox{3575 meters}$
