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In figure ( \( a \) ), mass \( 2 m \) is fixed on mass \( m \) which is attached to two springs of spring constant \( k \). In figure \( (b) \), mass \( m \) is attached to two spring of spring constant \( k \) and \( 2 k \) . If mass \( m \) in \( (a) \) and \( (b) \) are displaced by distance \( x \) horizontally and then released, then time period \( T_{1} \) and \( T_{2} \) corresponding to \( (a) \) and \( (b) \) respectively follow the relation.
(a)
(b)
(a) \( \frac{T_{1}}{T_{2}}=\frac{3}{\sqrt{2}} \)
(b) \( \frac{T_{1}}{T_{2}}=\sqrt{\frac{3}{2}} \)
(c) \( \frac{T_{1}}{T_{2}}=\sqrt{\frac{2}{3}} \)
(d) \( \frac{T_{1}}{T_{2}}=\frac{\sqrt{3}}{2} \)
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