$\mathrm{T}=\frac{1}{2} \mathrm{K}\left(\mathrm{A}^{2}-\mathrm{x}^{2}\right)$
$\frac{V}{T}=\frac{x^{2}}{A^{2}-x^{2}}$
${x}_{1}=5 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)$ 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.

Simultaneously at $t=0$, a small pebble is projected with speed $v$ from point $P$ at an angle of $45^{\circ}$ as shown in the figure. Point $P$ is at a horizontal distance of $10 \ cm$ from $O$. If the pebble hits the block at $t=1 \ s$, the value of $v$ is (take $g =10 \ m / s ^2$ )