A block of mass $m$ hangs from three springs having same spring constant $k$. If the mass is slightly displaced downwards, the time period of oscillation will be
$2 \pi \sqrt{\frac{m}{3 k}}$
$2 \pi \sqrt{\frac{3 m}{2 k}}$
$2 \pi \sqrt{\frac{2 m}{3 k}}$
$2 \pi \sqrt{\frac{3 k}{m}}$
A $100 \,g$ mass stretches a particular spring by $9.8 \,cm$, when suspended vertically from it. ....... $g$ large a mass must be attached to the spring if the period of vibration is to be $6.28 \,s$.
In the adjacent figure, if the incline plane is smooth and the springs are identical, then the period of oscillation of this body 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
$A$ block of mass $M_1$ is hanged by a light spring of force constant $k$ to the top bar of a reverse Uframe of mass $M_2$ on the floor. The block is pooled down from its equilibrium position by $a$ distance $x$ and then released. Find the minimum value of $x$ such that the reverse $U$ -frame will leave the floor momentarily.
Two bodies $M$ and $N $ of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude $M$ to that of $N$ is