$A$ bar of mass $m$ is suspended horizontally on two vertical springs of spring constant $k$ and $3k$. The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar (Neglect mass of springs and friction everywhere).

$A$ block $P$ of mass $m$ is placed on a smooth horizontal surface. $A$ block $Q$ of same mass is placed over the block $P$ and the coefficient of static friction between them is $\mu_S$. $A$ spring of spring constant $K$ is attached to block $Q$. The blocks are displaced together to a distance $A$ and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the blocks is

$A$ spring with a spring constant of $1200\, Nm^{-1}$ is mounted on a smooth frictionless surface and attached to a block of mass $3\, kg$. The block is pulled $2\, cm$ to the right and released. The angular frequency of oscillation is .... $rad/s$.

$A$ force of $6.4 \, N$ stretches a vertical spring by $0.1 \, m$. The mass that must be suspended from the spring so that it oscillates with a period of $\left( \frac{\pi}{4} \right) \, s$ is ... $kg$.

Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratio of the time period of oscillation of the two $SHM$ is $\frac{T_b}{T_a} = \sqrt{x}$,where the value of $x$ is (Round off to the Nearest Integer).

$A$ spring of force constant $k$ is cut into two parts whose lengths are in the ratio $1:2$. The two parts are now connected as shown and a block of mass $m$ is connected to the combined spring. Find the period of oscillation performed by the block.