In the figure,$S_1$ and $S_2$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed,the frequency will become

$A$ mass $m$ is suspended from a spring of force constant $k$ and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is

In the arrangement given in the figure,if the block of mass $m$ is displaced,the frequency is given by:

$A$ $1 \, kg$ block attached to a spring vibrates with a frequency of $1 \, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8 \, kg$ block placed on the same table. The frequency of vibration of the $8 \, kg$ block is ..... $Hz$.

The variation of potential energy of a harmonic oscillator is as shown in the figure. The spring constant is

$A$ body of mass $1 \,kg$ is suspended from a spring of negligible mass. Another body of mass $500 \,g$ moving vertically upwards hits the suspended body with a velocity of $3 \,ms^{-1}$ and gets embedded in it. If the frequency of oscillation of the system of the two bodies after collision is $\frac{10}{\pi} \,Hz$,the amplitude of the motion and the spring constant are respectively,