$A$ $10 \,kg$ metal block is attached to a spring of spring constant $1000 \,N \,m^{-1}$. The block is displaced from the equilibrium position by $10 \,cm$ and released. The maximum acceleration of the block is: (in $\,m/s^2$)

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).

$A$ block of mass $M_1$ is hung by a light spring of force constant $k$ from the top bar of a reverse $U$-frame of mass $M_2$ resting on the floor. The block is pulled down from its equilibrium position by a distance $x$ and then released. Find the minimum value of $x$ such that the reverse $U$-frame will leave the floor momentarily.

The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring is cut to half,the same mass oscillates with frequency $v_2$. The value of $v_2/v_1$ is . . . . . . .

Two identical springs of constant $K$ are connected in series and parallel as shown in the figure. $A$ mass $M$ is suspended from them. The ratio of their frequencies in series to parallel combination will be

$A$ mass at the end of a spring executes harmonic motion about an equilibrium position with an amplitude $A$. Its speed as it passes through the equilibrium position is $V$. If extended $2A$ and released,the speed of the mass passing through the equilibrium position will be