Answer
The period of the vibration is $13.5~s$
Work Step by Step
When the person swings at the end of the rope, the person is swinging like a pendulum. We can find the period of the vibration:
$T = 2\pi~\sqrt{\frac{L}{g}}$
$T = 2\pi~\sqrt{\frac{45~m}{9.80~m/s^2}}$
$T = 13.5~s$
The period of the vibration is $13.5~s$.
