Two massless springs of force constants $K_1$ and $K_2$ are joined end to end. The resultant force constant $K$ of the system is

$A$ particle of mass $m$ is attached to four springs with spring constants $k, k, 2k$ and $2k$ as shown in the figure. Four springs are attached to the four corners of a square and a particle is placed at the center. If the particle is pushed slightly towards any side of the square and released,the period of oscillation will be

Two identical springs of constant $k$ are connected in series and then in parallel. $A$ mass $m$ is suspended from them,the ratio of their frequencies of vertical oscillations will be

One end of a spring of force constant $k$ is fixed to a vertical wall and the other to a block of mass $m$ resting on a smooth horizontal surface. There is another wall at a distance $x_0$ from the block. The spring is then compressed by $2 x_0$ and released. The time taken by the block to strike the other wall is

$A$ block of mass $m$ attached to one end of a vertical spring produces an extension $x$. If the block is pulled and released,the periodic time of oscillation is:

Two identical springs are connected to a mass $m$ as shown in the figure ($k$ = spring constant). If the time period of the configuration in $(a)$ is $2 \,s$, what is the time period of the configuration in $(b)$?