A particle $\text{'}P\text{'}$ of mass $m$ is placed on a smooth horizontal surface is attached to three identical springs $A, B$ and $C$ each of force constant $K$ as shown in figure. If the particle is pushed slightly against spring $A$ and released. Find the time period of oscillation of the particle.

Find the time period of oscillation of the block of mass $m$ in case (I) . Consider the pulleys are light and small.

Find the time period of oscillation of the block of mass $m$ in case (I) . Consider the pulleys are light and small.

A block of mass $m$ hangs from a smooth fixed pulley $P,$ by an inextensible string filled with two springs of stiffness $k_1$ and $k_2.$ The string passes over a movable smooth light pulley $P_2$ which is connected with another ideal spring of stiffness $k_3$ Find the period of oscillation of the block.

The figure shows a particle of mass $\text{'}m\text{'},$ attached with four identical springs, each of length $l.$ Initial tension in each spring is $F_0.$ Neglecting gravity, calculate period of small oscillations of the particle along a line perpendicular to the plane of the figure.