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

$A$ body executes $SHM$ under the action of force $F_1$ with time period $T_1$. If the force is changed to $F_2$,it executes $SHM$ with time period $T_2$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,its time period is:

Two masses $m_1$ and $m_2$ connected by a spring of spring constant $k$ rest on a frictionless surface. If the masses are pulled apart and let go,the time period of oscillation is

If a body of mass $0.98\, kg$ is made to oscillate on a spring of force constant $4.84\, N/m$,the angular frequency of the body is ..... $rad/s$. (in $.22$)

$A$ solid sphere of mass $M$ and radius $R$ is attached to a spring of negligible mass kept on a horizontal plane such that it can roll without slipping. The sphere is made to execute $SHM$ by stretching it through a distance and releasing it. The time period of such oscillation is ($K=$ spring constant).

One end of a long metallic wire of length $L$,area of cross-section $A$,and Young's modulus $Y$ is tied to the ceiling. The other end is tied to a massless spring of force constant $K$. $A$ mass $m$ hangs freely from the free end of the spring. It is slightly pulled down and released. Its time period is given by