In the situation as shown in the figure,the time period of vertical oscillation of the block for small displacements will be:

$A$ stiff spring having spring constant $k = 400 \text{ N/m}$ is attached to the floor vertically. $A$ mass $m = 10 \text{ kg}$ is placed on top of the spring. The block oscillates if it is pressed downward and released. Find the extension in the spring at which the block loses contact with the spring. (Take $g = 10 \text{ m/s}^2$) (in $\text{ cm}$)

In the given figure,a body of mass $M$ is held between two massless springs on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has a spring constant $k,$ the frequency of oscillation of the given body is:

$A$ block of mass $1 \; kg$ is fastened to a spring with a spring constant of $50 \; N m^{-1}$. The block is pulled to a distance $x = 10 \; cm$ from its equilibrium position at $x = 0$ on a frictionless surface and released from rest at $t = 0$. Calculate the kinetic,potential,and total energies of the block when it is $5 \; cm$ away from the mean position.

$A$ light spring is suspended with mass $m_1$ at its lower end and its upper end 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 $m_1 : m_2$ is

As per the given figures,two springs of spring constants $K$ and $2K$ are connected to a mass $m$. If the period of oscillation in figure $(a)$ is $3 \text{ s}$,then the period of oscillation in figure $(b)$ will be $\sqrt{x} \text{ s}$. The value of $x$ is $.........$