An ideal spring with spring-constant $K$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

A force of $6.4\  N$ stretches a vertical spring by $0.1\ m$. The mass that must be suspended  from the spring so that it oscillates with a time period of $\pi/4\  second$ is .... $kg$

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

Two identical springs have the same force constant $73.5 \,Nm ^{-1}$. The elongation produced in each spring in three cases shown in Figure-$1$, Figure-$2$ and Figure-$3$ are $\left(g=9.8 \,ms ^{-2}\right)$

An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant, the springs are relaxed. The left mass is displaced to the/left and theiright mass is displaced to the right by same distance and released. The resulting collision is elastic. The time period of the oscillations of system is

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