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 $s$)

$A$ spring-mass system vibrates such that the mass travels on a surface with a coefficient of friction $\mu$. The mass is released after compressing the spring by a distance $a$ and it travels up to a distance $b$ after its equilibrium position. Then,while traveling from $x = -a$ to $x = b$,the reduction in its amplitude will be:

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

All the springs in figures $(a)$,$(b)$,and $(c)$ are identical,each having a force constant $K$. $A$ mass $m$ is attached to each system. If $T_a, T_b$,and $T_c$ are the time periods of oscillations of the three systems in figures $(a)$,$(b)$,and $(c)$ respectively,then:

$A$ block of mass $m$,attached to a spring of spring constant $k$,oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed $v$ when the spring is at its natural length. Before coming to an instantaneous rest,if the block moves a distance $x$ from the mean position,then

Initially,the system is in equilibrium. The time period of $SHM$ of the block in the vertical direction is