${x}_{1}=5 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)$ and ${x}_{2}=5 \sqrt{2}(\sin 2 \pi {t}+\cos 2 \pi {t})$
The amplitude of second motion is ....... times the amplitude in first motion.



Statement $I :$ A second's pendulum has a time period of $1$ second.
Statement $II :$ It takes precisely one second to move between the two extreme positions.
In the light of the above statements, choose the correct answer from the options given below: