Physics - SHM Question with Solution | TestHub

The velocity of$1 kg$block just before striking

$V=\sqrt{2\times 10\times 100}=20\sqrt{5}\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$

Applying conservation of momentum, the blocks stick after the collision and move with velocity$v$

Or$1\times 20\sqrt{5}=4v$

Final velocity$v=5\sqrt{5}$,

Using energy conservation

$KE+PE=$const

$\frac{1}{2}\times 4\times {\left(5\sqrt{5}\right)}^2+\frac{1}{2}k{\left(\frac{3g}{k}\right)}^2$

$=0+\frac{1}{2}k.x^2$

$\therefore x^2=\frac{4\times 25\times 5}{1.25\times {10}^6}+\frac{30\times 30}{{\left(1.25\times {10}^6\right)}^2}$

$x=\frac{20}{1000} \mathrm{m}=2 \mathrm{cm}$