What will be the force constant of the spring system shown in the figure?

$A$ particle of mass $m$ is attached to $3$ springs $A$,$B$ and $C$ of equal force constant $K$ as shown in the figure. If the particle is pushed slightly along the line of spring $C$ and released,find the period of oscillation.

When a mass $m$ is attached to a spring,it normally extends by $0.2\, m$. If the mass $m$ is given a slight additional extension and released,what will be its time period?

$A$ heavy brass sphere is hung from a spring and it executes vertical vibrations with period $T$. The sphere is now immersed in a non-viscous liquid with a density $(1/10)^{\text{th}}$ that of brass. When set into vertical vibrations with the sphere remaining inside the liquid all the time,the time period will be

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in the figure. Show that when the mass is displaced from its equilibrium position on either side,it executes simple harmonic motion. Find the period of oscillations.

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