An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is $15\, cm/sec$ and the period is $628$ milli-seconds. The amplitude of the motion in centimeters is

Five identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations (i), (ii) and (iii) are in the ratio

One-forth length of a spring of force constant $K$ is cut away. The force constant of the remaining spring will be

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

If the period of oscillation of mass $m$ suspended from a spring is $2\, sec$, then the period of mass $4m$ will be  .... $\sec$

The length of a spring is $l$ and its force constant is $k$. When a weight $W$ is suspended from it, its length increases by $x$. If the spring is cut into two equal parts and put in parallel and the same weight $W$ is suspended from them, then the extension will be