The effective spring constant of the two-spring system as shown in the figure will be:

$A$ body of mass $100 \ g$ is tied to a spring of spring constant $8 \ N/m$,while the other end of the spring is fixed. If the body moves in a circular path on a smooth horizontal surface with a constant angular speed of $8 \ rad/s$,then the ratio of the extension in the spring to its natural length will be: (in $:1$)

Two springs of force constants $K$ and $2K$ are connected to a mass $m$ as shown in the figure. The frequency of oscillation of the mass is:

$A$ 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:

$A$ mass $m$ attached to a spring oscillates with a period of $3\,s$. If the mass is increased by $1\,kg$,the period increases by $1\,s$. The initial mass $m$ is

$A$ system consisting of three masses attached to a spring is in equilibrium. When the $700\,g$ mass is removed,the system oscillates with a period of $3\,s$. When the $500\,g$ mass is also removed,what will be the new time period of the system? (in $\text{seconds}$)