A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S.H.M.$ of time period $T$. If the mass is increased by m, the time period becomes $5T/3$. Then the ratio of $m/M$ is

A spring of force constant $k$ is cut into lengths of ratio $1:2:3$ . They are connected in series and the new force constant is $k'$ . Then they are connected in parallel and force constant is $k''$ . Then $k':k''$ is

A mass $m = 8\,kg$ is attahced to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is $200\,N/m$. The mass $m$ is then released and begins to undergo small oscillations. The maximum velocity of the mass will be ..... $m/s$ $(g = 10\,m/s^2)$

Initially system is in equilibrium. Time period of $SHM$ of block in vertical direction is

Is the following Statement True or False ?

$1.$ If the spring is cut in two equal piece the spring constant of every piece decreases.

$2.$ Displacement of $SHO$ increases, its acceleration decrease. 

$3.$ A system can happen to oscillate, have more than one natural frequency.

$4.$ The periodic time of $SHM$ depend on amplitude or energy or phase constant.

When a mass $m$ is attached to a spring, it normally extends by $0.2\, m$. The mass $m$ is given a slight addition extension and released, then its time period will be