$A$ rectangular block of mass $5\,kg$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1\,m$ and time period $3.14\,s$. The maximum force exerted by the spring on the block is $.......N$.

Find the maximum amplitude for safe $SHM$ (the block does not topple during $SHM$) of a cubical block of side $a$ on a smooth horizontal floor as shown in the figure (the spring is massless). The spring is attached at a height of $2a/3$ from the floor.

$A$ mass of $0.2\,kg$ is attached to the lower end of a massless spring of force-constant $200\,N/m,$ the upper end of which is fixed to a rigid support. Which of the following statements is/are true?

$A$ 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 ... $kg$.

$A$ spring of length $l$ and force constant $k$ is attached to a mass $m$ and oscillates with frequency $f_1$. If the spring is cut into two equal parts and one part is attached to the same mass $m$ to oscillate,its frequency becomes $f_2$. Find the relation between $f_1$ and $f_2$.

$A$ uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended,with its length vertical,from a fixed point by a massless spring,such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. When the cylinder is given a downward push and released,it starts oscillating vertically with a small amplitude. The time period $T$ of the oscillations of the cylinder will be