$A$ spring has a certain mass suspended from it and its period for vertical oscillations is $T_1$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now $T_2$. The ratio $T_1 / T_2$ is

Let $T_1$ and $T_2$ be the time periods of two springs $A$ and $B$ when a mass $m$ is suspended from them separately. Now both the springs are connected in parallel and the same mass $m$ is suspended with them. If $T$ is the new time period in this position,then:

As shown in the figure, a block of weight $20 \,N$ is connected to the top of a smooth inclined plane by a massless spring of constant $8 \pi^2 \,Nm^{-1}$. If the block is pulled slightly from its mean position and released, the period of oscillations is (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,s$)

The effective spring constant of the two-spring system as shown in the figure will be:

In the provided figure,two bodies $A$ and $B$ of masses $200 \, g$ and $800 \, g$ are attached to a system of springs. The springs are kept in a stretched position when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be $..... \, rad/s$ when $k = 20 \, N/m$.

The equivalent spring constant of the system as shown in the figure will be: