$A$ block of mass $M$ rests on a piston executing $S.H.M.$ with a period of $1 \,s$. The amplitude of oscillations, such that the mass is separated from the piston, is (acceleration due to gravity, $g=10 \,m/s^2$, $\pi^2=10$)

$A$ 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?

When a block of mass $m$ is suspended separately by two different springs having time periods $t_1$ and $t_2$,respectively. If the same mass is connected to the series combination of both springs,then its time period is given by:

The vertical extension in a light spring by a weight of $1\, kg$ suspended from the wire is $9.8\, cm$. What is the period of oscillation?

$A$ cylindrical block of density $\rho$ is partially immersed in a liquid of density $3\rho$. The plane surface of the block remains parallel to the surface of the liquid. The height of the block is $60\, cm$. The block performs $SHM$ when displaced from its mean position. [Use $g = 9.8\, m/s^2$]

$A$ light spring is suspended with mass $m_1$ at its lower end and its upper end is fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is $T$ seconds. When a mass $m_2$ is added to $m_1$ and the system is made to oscillate, the period is found to be $\frac{3}{2} T$. The ratio $\frac{m_1}{m_2}$ is