In the arrangement, spring constant $k$ has value $2\,N\,m^{-1}$ , mass $M = 3\,kg$ and mass $m = 1\,kg$ . Mass $M$ is in contact with a smooth surface. The coefficient of friction between two blocks is $0.1$ . The time period of $SHM$ executed by the system is

A uniform stick of mass $M$ and length $L$ is pivoted at its centre. Its ends are tied to two springs each of force constant $K$ . In the position shown in figure, the strings are in their natural length. When the stick is displaced through a small angle $\theta $ and released. The stick

A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K _1$ and $K _2$. For the frictionless surface, the time period of oscillation of mass $m$ is

A body of mass $5\; kg$ hangs from a spring and oscillates with a time period of $2\pi $ seconds. If the ball is removed, the length of the spring will decrease by

A force of $20\,dyne$ applied to the end of spring increase its length of $1\, mm$, then force constant will be what ?