$A$ particle of mass $m$ is attached to three identical springs $A, B$ and $C$ each of force constant $k$ as shown in the figure. If the particle of mass $m$ is pushed slightly against the spring $A$ and released,then the time period of oscillations is

$A$ block of mass $2 \ kg$ is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is $2 \ m$ and the spring constant is $200 \ N/m$. The block is pushed such that the length of the spring becomes $1 \ m$ and then released. At a distance $x \ m \ (x < 2)$ from the wall,the speed of the block will be:

Two bodies $A$ and $B$ of equal mass are suspended from two separate massless springs of spring constants $K_1$ and $K_2$ respectively. The two bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitude of $B$ to that of $A$ is

$A$ block of mass $m$ has two similar rubber ribbons attached to it as shown in the figure. The force constant of each rubber ribbon is $K$ and the surface is frictionless. The block is displaced from the mean position by $x$ and released. At the mean position,the ribbons are undeformed. The vibration period is

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.

$A$ coin is placed on a horizontal platform. The platform performs vertical simple harmonic motion with an angular frequency $\omega$. The amplitude of oscillation is gradually increased. At what condition will the coin first lose contact with the platform?