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

$A$ spring has a certain mass suspended from it and its period for vertical oscillation is $T$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now

$A$ body of mass $m$ is suspended to an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

$A$ mass $m_1$ connected to a horizontal spring performs $S.H.M.$ with amplitude $A$. While mass $m_1$ is passing through the mean position,another mass $m_2$ is placed on it so that both the masses move together with amplitude $A_1$. The ratio of $\frac{A_1}{A}$ is:

$A$ block of mass $2\,kg$ is attached to two identical springs,each with a spring constant of $20\,N/m$. The block is placed on a frictionless surface,and the outer ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position,it executes simple harmonic motion. The time period of oscillation is $\frac{\pi}{\sqrt{x}}$ in $SI$ units. The value of $x$ is $..........$

$A$ block of mass $m$ is suspended separately by two different springs having time periods $t_1$ and $t_2$. If the same mass is connected to a parallel combination of both springs,then its time period will be