$A$ spring has a certain mass suspended from it and its period of vertical oscillations is $T_1$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now $T_2$. The ratio of $T_2 / T_1$ is

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

When a mass $m$ is connected individually with two springs $S_1$ and $S_2$,the oscillation frequencies are $n_1$ and $n_2$. If the mass $m$ is attached to the springs as shown in the figure,the oscillation frequency would be

$A$ spring-mass system vibrates such that the mass travels on a surface with a coefficient of friction $\mu$. The mass is released after compressing the spring by a distance $a$ and it travels up to a distance $b$ after its equilibrium position. Then,while traveling from $x = -a$ to $x = b$,the reduction in its amplitude will be:

$A$ mass $m$ is suspended from two coupled springs connected in series. The force constants for the springs are $K_1$ and $K_2$. The time period of the suspended mass will be:

The upper end of the spring is fixed and a mass $m$ is attached to its lower end. When the mass is slightly pulled down and released,it oscillates with a time period of $3 \text{ s}$. If the mass $m$ is increased by $1 \text{ kg}$,the time period becomes $5 \text{ s}$. The value of $m$ is (mass of the spring is negligible).