$A$ particle of mass $m$ is attached to three identical massless springs of spring constant $k$ as shown in the figure. The time period of vertical oscillation of the particle is

$A$ solid cylinder of mass $m$ and volume $V$ is suspended from the ceiling by a spring of spring constant $k$. It has a cross-sectional area $A$. It is submerged in a liquid of density $\rho$ up to half its length. If a small block of mass $M_0$ is kept at the center of the top, the amplitude of small oscillation will be:

$A$ mass of $2 \, kg$ is attached to a spring with a spring constant of $50 \, N/m$. The block is pulled to a distance of $5 \, cm$ from its equilibrium position at $x = 0$ on a horizontal frictionless surface and released from rest at $t = 0$. Write the expression for its displacement at any time $t$.

$A$ spring has a certain mass suspended from it and its period for vertical oscillation is $T$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now

$A$ mass $m$ is suspended from two coupled springs connected in series. The force constants for the springs are $K_1$ and $K_2$. The time period of the suspended mass will be:

$A$ mass $m$ is attached to two springs as shown in the figure. The spring constants of the two springs are $K_1$ and $K_2$. For the frictionless surface,the time period of oscillation of mass $m$ is