The scale of a spring balance reading from $0$ to $10 \, kg$ is $0.25 \, m$ long. $A$ body suspended from the balance oscillates vertically with a period of $\pi / 10 \, s$. The mass suspended is ..... $kg$ (neglect the mass of the spring).

$A$ 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?

$A$ 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 time period of $\pi/4 \ s$ is .... $kg$.

$A$ mass $M$,attached to a horizontal spring,executes $S.H.M.$ with amplitude $A_1$. When the mass $M$ passes through its mean position,a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\frac{A_1}{A_2}$ is

$A$ clock is designed based on the oscillations of a spring-block system suspended vertically in the absence of air resistance. Assume it shows the correct time when a spring of stiffness $k$ and a block of mass $m$ are used. If the block is replaced by another block of mass $4m$, choose the correct option.

$A$ block of mass $m$ is attached to two springs of spring constants $k_1$ and $k_2$ as shown in the figure. The block is displaced by $x$ towards the right and released. The velocity of the block when it is at $x/2$ will be