Three masses $700g, 500g$ and $400g$ are suspended at the end of a spring a shown  and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a  period of $3\,seconds$, when the $500g$ mass is also removed, it will oscillate with a period of .... $s$

In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k,$ the frequency of oscillation of given body is :

In the figure, ${S_1}$ and ${S_2}$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed, the frequency will become

Aheavy brass sphere is hung from a light spring and is set in vertical small oscillation with a period $T.$ The sphere is now immersed in a non-viscous liquid with a density $1/10\,th$ the density of the sphere. If the system is now set in vertical $S.H.M.,$ its period will be

In the situation as shown in figure time period of vertical oscillation of block for small displacements will be 

Two particles of mass $m$ are constrained to move along two horizontal frictionless rails that make an angle $2\theta $ with respect to each other. They are connected by a spring with spring constant $k$ . The angular frequency of small oscillations for the motion where the two masses always stay parallel to each other (that is the distance between the meeting point of the rails and each particle is equal) is