$A$ 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 ..... $kg$.

On a smooth inclined plane,a block of mass $M$ is fixed to two rigid supports using two springs,as shown in the figure. If each spring has spring constant $k$,then the period of oscillation of the block is (Neglect the masses of the springs)

In the provided figure,two bodies $A$ and $B$ of masses $200 \, g$ and $800 \, g$ are attached to a system of springs. The springs are kept in a stretched position when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be $..... \, rad/s$ when $k = 20 \, N/m$.

$A$ mass of $0.2\,kg$ is attached to the lower end of a massless spring of force-constant $200\,N/m,$ the upper end of which is fixed to a rigid support. Which of the following statements is/are true?

Two springs of spring constants $k_1$ and $k_2$ are connected to a mass $m$ as shown in the figure. Under negligible friction, if the mass is displaced by a small amount $x$ from its equilibrium position and released, the period of oscillation is

Two springs,of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$. If both $k_1$ and $k_2$ are made four times their original values,the frequency of oscillation becomes