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 (

Question

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.

TestHub · Accepted Answer

The time period of spring block system is given by $T = 2 π \sqrt{\frac{m}{k}}$ .
In both the cases springs are connected in parallel,
In case $1$ : $k_{e q} = 2 k$ and total mass is $3 m$ . Therefore,
$T_{1} = 2 π \sqrt{\frac{(3 m)}{k_{e q}}} = 2 π \sqrt{\frac{(3 m)}{2 k}}$
In case $2 :$ $k_{e q} = 3 k$ and total mass is $m$ . Therefore,
$T_{2} = 2 π \sqrt{\frac{(m)}{3 k}}$
$\Rightarrow \frac{T_{1}}{T_{2}} = \sqrt{\frac{9}{2}} = \frac{3}{\sqrt{2}}$

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