$A$ particle of mass $m$ is attached to three identical massless springs of spring constant $k$ as shown in the figure. The time period of vertical oscillation of the particle 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 the amplitude of $A$ and $B$ is

$A$ mass $m$ is suspended from a spring of length $l$ and force constant $K$. The frequency of vibration of the mass is $f_1$. The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of the mass is $f_2$. Which of the following relations between the frequencies is correct?

$A$ block of mass $M$ rests on a piston executing $S.H.M.$ with a period of $1 \,s$. The amplitude of oscillations, such that the mass is separated from the piston, is (acceleration due to gravity, $g=10 \,m/s^2$, $\pi^2=10$)

Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed supports (see figure). When the mass is displaced from the equilibrium position on either side,it executes simple harmonic motion. The time period of oscillations of this system is ...... .

The effective spring constant of the two-spring system as shown in the figure will be: