A block of mass $m$ is at rest on an another block of same mass as shown in figure. Lower block is attached to the spring, then the maximum amplitude of motion so that both the block will remain in contact is

- A
$\frac{{mg}}{{2K}}$

- B
$\frac{{mg}}{{K}}$

- C
$\frac{{2mg}}{{K}}$

- D
$\frac{{3mg}}{{K}}$

Find the time period of mass $M$ when displaced from its equilibrium position and then released for the system shown in figure.

A mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n$. What will be the frequency of the system if a mass $4 m$ is suspended from the same spring

- [AIPMT 1998]

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

- [AIIMS 1998]

A spring having with a spring constant $1200\; N m ^{-1}$ is mounted on a hortzontal table as shown in Figure A mass of $3 \;kg$ is attached to the free end of the spring. The mass is then pulled sideways to a distance of $2.0 \;cm$ and released

let us take the position of mass when the spring is unstreched as $x=0,$ and the direction from left to right as the positive direction of $x$ -axis. Give $x$ as a function of time $t$ for the oscillating mass if at the moment we start the stopwatch $(t=0),$ the mass is

$(a)$ at the mean position,

$(b)$ at the maximum stretched position, and

$(c)$ at the maximum compressed position. In what way do these functions for $SHM$ differ from each other, in frequency, in amplitude or the inittal phase?

Two particles of mass $m$ are constrained to move along two horizontal frictionless rails that make an angle $2\theta $ with respect to each other. They are connected by a spring with spring constant $k$ . The angular frequency of small oscillations for the motion where the two masses always stay parallel to each other (that is the distance between the meeting point of the rails and each particle is equal) is