$A$ spring of force constant $k$ is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of

$A$ 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 $.......N$.

$A$ 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?

$A$ mass of $2.0\, kg$ is placed on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released,the mass executes simple harmonic motion. The spring constant is $200\, N/m$. What should be the minimum amplitude of the motion so that the mass gets detached from the pan? (Take $g = 10\, m/s^2$)

$A$ mass $m$ is suspended from a spring of negligible mass. The spring is pulled a little and then released,so that the mass executes $S.H.M.$ with a time period $T$. If the mass is increased by $m_0$,the time period becomes $\frac{5T}{4}$. The ratio $\frac{m_0}{m}$ is

$A$ body of mass $4 \ kg$ attached to a spring of force constant $64 \ N \ m^{-1}$ executes simple harmonic motion on a frictionless horizontal surface. The time period of oscillation is