$A$ mass $m$ is attached to two springs as shown in the figure. The spring constants of the two springs are $K_1$ and $K_2$. For the frictionless surface,the time period of oscillation of mass $m$ is

$A$ uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended,with its length vertical,from a fixed point by a massless spring,such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. When the cylinder is given a downward push and released,it starts oscillating vertically with a small amplitude. The time period $T$ of the oscillations of the cylinder will be

$A$ body of mass $m$ is suspended to an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

$A$ block is placed on a frictionless horizontal table. The mass of the block is $m$ and springs are attached on either side with force constants $K_1$ and $K_2$. If the block is displaced a little and left to oscillate,then the angular frequency of oscillation will be

Three masses $500 \ g$,$300 \ g$,and $100 \ g$ are suspended at the end of a spring as shown in the figure and are in equilibrium. When the $500 \ g$ mass is removed,the system oscillates with a period of $2 \ s$. When the $300 \ g$ mass is also removed,it will oscillate with a period of (in $s$)

$A$ body of mass $m$ is attached to the lower end of a spring whose upper end is fixed. The mass of the spring is negligible. When the mass $m$ is pulled down slightly and released,it oscillates with a time period of $3 \ s$. When the mass $m$ is increased by $1 \ kg$,the time period of oscillation becomes $5 \ s$. What is the value of $m$ in $kg$?