Question

In the reported figure, two bodies $A$ and $B$ of masses $200g$ and $800g$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be ______$rad/s$ when $k=20N/m$.

Answer 1

Answer: 10

$\omega =\sqrt{\frac{k_{eq}}{\mu }}$
$\mu =$ reduced mass
springs are in series connection
$k_{eq}=\frac{k_1{k}_2}{k_1+k_2}$
$k_{eq}=\frac{k\times 4k}{5k}=\frac{4k}{5}$
$k_{eq}=\frac{4\times 20}{5}N/m=16N/m$
$\mu =\frac{m_1{m}_2}{m_1+m_2}=\frac{0.2\times 0.8}{0.2+0.8}$
$=0.16kg$
$\omega =\sqrt{\frac{16}{0.16}}=\sqrt{100}=10$