Two identical point masses $P$ and $Q$,suspended from two separate massless springs of spring constants $k_1$ and $k_2$,respectively,oscillate vertically. If their maximum speeds are the same,the ratio $(A_Q / A_P)$ of the amplitude $A_Q$ of mass $Q$ to the amplitude $A_P$ of mass $P$ is

Five identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations $(i)$,$(ii)$ and $(iii)$ are in the ratio

$A$ solid sphere of mass $M$ and radius $R$ is attached to a spring of negligible mass kept on a horizontal plane such that it can roll without slipping. The sphere is made to execute $SHM$ by stretching it through a distance and releasing it. The time period of such oscillation is ($K=$ spring constant).

$A$ 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 $g = 10\, m/s^2$)

If $A$ is the area of cross-section of a spring,$L$ is its length,$E$ is the Young's modulus of the material of the spring,then the time period and force constant of the spring will be respectively:

If the period of oscillation of mass $m$ suspended from a spring is $2 \ s$,then the period of oscillation of suspended mass $4m$ with the same spring will be: (in $s$)