$A$ block of mass $m$ is at rest on another block of the same mass as shown in the figure. The lower block is attached to a spring. What is the maximum amplitude of motion such that both blocks remain in contact?

$A$ body of mass $m$ is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand,so that the spring is neither stretched nor compressed. Suddenly,the support of the hand is removed. The lowest position attained by the mass during oscillation is $4 \, cm$ below the point where it was held in hand.
$(a)$ What is the amplitude of oscillation?
$(b)$ Find the frequency of oscillation.

Two identical springs of constant $k$ are connected in series and then in parallel. $A$ mass $m$ is suspended from them,the ratio of their frequencies of vertical oscillations will be

$A$ mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S.H.M.$ of period $T$. If the mass is increased by $m$,the time period becomes $\frac{5T}{3}$. What is the ratio $\left(\frac{M}{m}\right)$?

As shown in the figure, a block of weight $20 \,N$ is connected to the top of a smooth inclined plane by a massless spring of constant $8 \pi^2 \,Nm^{-1}$. If the block is pulled slightly from its mean position and released, the period of oscillations is (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,s$)

When a body of mass $8 \,kg$ is attached to a spring balance, the reading of the balance is $20 \,cm$. Instead of $8 \,kg$, if another body of mass $M$ is suspended from the spring balance and is made to oscillate vertically, the time period of oscillation is $\frac{\pi}{5} \,s$, then the value of $M$ is (Acceleration due to gravity $= 10 \,m/s^2$) (in $\,kg$)