$A$ mass $m$ attached to a spring oscillates every $2 \, s$. If the mass is increased by $2 \, kg$,then the time period increases by $1 \, s$. The initial mass is ..... $kg$.

Two identical springs of constant $K$ are connected in series and parallel as shown in the figure. $A$ mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will be

$A$ mass $m$ is attached to two springs of same force constant $K$,as shown in the following four arrangements. If $T_1, T_2, T_3$ and $T_4$ are the time periods of oscillation in the respective arrangements,in which case is the time period maximum?

Two bodies $A$ and $B$ of equal mass are suspended from two massless springs of spring constant $k_1$ and $k_2$,respectively. If the bodies oscillate vertically such that their amplitudes are equal,the ratio of the maximum velocity of $A$ to the maximum velocity of $B$ is

$A$ uniform circular disc of mass $12 \ kg$ is held by two identical springs. When the disc is slightly pressed down and released,it executes $S.H.M.$ of period $2 \ s$. The force constant of each spring is (nearly) (Take $\pi^2=10$) (in $Nm^{-1}$)

When a mass $m$ is connected individually with two springs $S_1$ and $S_2$,the oscillation frequencies are $n_1$ and $n_2$. If the mass $m$ is attached to the springs as shown in the figure,the oscillation frequency would be