$(a)\;1\;rad/s\qquad(b)\;2\;rad/s\qquad(c)\;1.5\;rad/s\qquad(d)\;0.5\;rad/s$

Oscillations

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Answer : (a) $\;1\;rad/s$

Explanation :

First $\;3 \times 6\;$ and $\;6 \times 12\;$ are in series

Therefore , $\;\large\frac{3 \times 6}{9}\;$ and $\;\large\frac{6 \times12}{18}\;$ are in parallel

Therefore, the equivalent spring constant of the system is $\;2+4=6 N/m$

The angular frequency $\;w=\sqrt{\large\frac{K}{m}}$

$=\sqrt{\large\frac{6}{6}}$

$=1$

$w=1\; rad/s\;.$

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