The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended,the period of oscillation will now be

$A$ mass $x \ g$ is suspended from a light spring. It is pulled in a downward direction and released so that the mass performs $S.H.M.$ of period $T$. If the mass is increased by $Y \ g$,the period becomes $4T/3$. The ratio of $Y/x$ is:

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2$,respectively. If the maximum velocities during oscillations are equal,the ratio of amplitudes of $A$ and $B$ is

$A$ $5\; kg$ collar is attached to a spring of spring constant $500\; N m^{-1}$. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by $10.0\; cm$ and released. Calculate
$(a)$ the period of oscillation.
$(b)$ the maximum speed and
$(c)$ maximum acceleration of the collar.

$A$ 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

As shown in the figure,two blocks of masses $m_1$ and $m_2$ are connected to a spring of force constant $k$. The blocks are slightly displaced in opposite directions to $x_1$ and $x_2$ distances and released. If the system executes simple harmonic motion,then the angular frequency of oscillation of the system $(\omega)$ is: