$A$ mass $m$ attached to the free end of a spring executes $SHM$ with a period of $1\; s$. If the mass is increased by $3\; kg$,the period of oscillation increases by $1\; s$. The value of mass $m$ is $..............kg$.

$A$ spring of length $l$ and force constant $k$ is attached to a mass $m$ and oscillates with frequency $f_1$. If the spring is cut into two equal parts and one part is attached to the same mass $m$ to oscillate,its frequency becomes $f_2$. Find the relation between $f_1$ and $f_2$.

Two particles $A$ and $B$ of masses $m$ and $2m$ are suspended from massless springs of force constants $K_1$ and $K_2$. During their oscillation, if their maximum velocities are equal, then the ratio of amplitudes of $A$ and $B$ is

$A$ block with mass $M$ is connected by a massless spring with stiffness constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_0$. Consider two cases: $(i)$ when the block is at $x_0$; and $(ii)$ when the block is at $x = x_0 + A$. In both cases, a particle with mass $m$ is placed on the mass $M$. Which of the following statements are correct?

The potential energy of a particle of mass $0.02 \ kg$ moving along the $x$-axis is given by $V = A x(x-4) \ J$, where $x$ is in metres and $A$ is a constant. Which of the following is/are correct statement$(s)$?

To make the frequency of an oscillator double,we have to