$A$ $5\, kg$ collar is attached to a spring of spring constant $500\, N/m$. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by $10\, cm$ and released. The time period of oscillation is

$A$ mass $M$ is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period

Two bodies $A$ and $B$ of equal mass are suspended from two separate massless springs of spring constants $K_1$ and $K_2$ respectively. The two bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitude of $B$ to that of $A$ is

$A$ plank with a small block on top of it is undergoing vertical $SHM$. Its period is $2 \ s$. The minimum amplitude at which the block will separate from the plank is:

$A$ block of mass $m$ attached to a massless spring is performing oscillatory motion of amplitude $A$ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point,the amplitude of oscillation for the remaining system becomes $fA$. The value of $f$ is

$A$ mass hangs from a spring and oscillates vertically. The top end of the spring is attached to the top of a box,and the box is placed on a scale,as shown in the figure. The reading on the scale is largest when the mass is