In the reported figure, two bodies $A$ and $B$ of masses $200\, {g}$ and $800\, {g}$ 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 ${k}=20 \,{N} / {m} .$
JEE MAIN 2021, Diffcult
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$\omega=\sqrt{\frac{k_{\text {eq }}}{\mu}}$
$\mu=$ reduced mass
springs are in series connection
$k _{eq}=\frac{ k _{1} k _{2}}{ k _{1}+ k _{2}}$
$k _{ eq }=\frac{ k \times 4 k }{5 k }=\frac{4 k }{5}$
$k _{ eq }=\frac{4 \times 20}{5} N / m =16 N / m$
$\mu=\frac{ m _{1} m _{2}}{ m _{1}+ m _{2}}=\frac{0.2 \times 0.8}{0.2+0.8}=0.16 kg$
$\omega=\sqrt{\frac{16}{0.16}}=\sqrt{100}=10$
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