Three masses $700 \mathrm{g}$, $500 \mathrm{g}$ and $400 \mathrm{g}$ are suspended at the end of a spring as shown and are in equilibrium. When the $700 \mathrm{g}$ mass is removed, the system oscillates with a period of $3$ $\sec$, and when the $500 \mathrm{gm}$ mass is also removed, it will oscillate with a period of 

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 the figure). If the mass $M$ is displaced in the horizontal direction, then the frequency of oscillation of the system is

Two identical springs are attached to a small block $P$. The other ends of the springs are fixed at $A$ and $B$. When $P$ is in equilibrium the extension of top spring is $20 \mathrm{cm}$ and extension of bottom spring is $10 \mathrm{cm}$. The period of small vertical oscillations of $P$ about its equilibrium position is (use $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$).

The below figure shows a system consisting of a massless pulley, a spring of force constant $k$ and a block of mass $m$. If the block is slightly displaced vertically downward from its equilibrium position and then released, the period of its vertical oscillation is

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

The springs shown in the figure are all up stretched in the beginning when a man starts pulling the block. The man exerts a constant force $F$ on the block.

A $1 \mathrm{kg}$ block is executing simple harmonic motion of amplitude $0.1 \mathrm{m}$ on a smooth horizontal surface under the restoring force of a spring of spring constant $100 \mathrm{N} \mathrm{m}$. A block of mass $3 \mathrm{kg}$ is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, then