The springs shown in the figure are identical,each having a spring constant $K$. When mass $A = 4\, kg$ is attached,the elongation of the spring is $1\, cm$. If mass $B = 6\, kg$ is attached to the system of two springs in series as shown,the total elongation produced is ..... $cm$.

$A$ block $A$ of mass $1\, kg$ is connected to two identical springs of spring constant $800\, N/m$ and is placed on a smooth horizontal surface as shown in the figure. Initially,the springs are relaxed. Now,the block $A$ is slightly displaced to the left and released. The time period of oscillation of the system is

$A$ mass $m = 1.0\,kg$ is placed on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released,the mass executes simple harmonic motion. The spring constant is $k = 500\,N/m$. What is the amplitude $A$ of the motion,so that the mass $m$ tends to get detached from the pan? (Take $g = 10\,m/s^2$).

The vertical extension in a light spring by a weight of $1\, kg$ suspended from it is $9.8\, cm$. What is the period of oscillation?

$A$ mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S.H.M.$ of time period $T$. If the mass is increased by $m$,the time period becomes $5T/3$. Then the ratio of $m/M$ is

On a smooth inclined plane,a block of mass $M$ is fixed to two rigid supports using two springs,as shown in the figure. If each spring has spring constant $k$,then the period of oscillation of the block is (Neglect the masses of the springs)