A block of mass $m$ is at rest on an another block of same mass as shown in figure. Lower block is attached to the spring, then the maximum amplitude of motion so that both the block will remain in contact is

Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.06 m. Each spring has a natural length of 0.06$\pi$ m and force constant 0.1N/m. Initially both the balls are displaced by an angle $\theta = \pi /6$ radian with respect to the diameter $PQ$ of the circle and released from rest. The frequency of oscillation of the ball B is

Four massless springs whose force constants are $2k, 2k, k$ and $2k$ respectively are attached to a mass $M$ kept on a frictionless plane (as shown in figure). If the mass $M$ is displaced in the horizontal direction, then the frequency of oscillation of the system is

If the period of oscillation of mass $m$ suspended from a spring is $2\, sec$, then the period of mass $4m$ will be  .... $\sec$

A mass $m$ is suspended from a spring of force constant $k$ and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is 

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