An object of mass $2 \,kg$ is attached to a spring with spring constant $8 \,N/m$. If the object is executing simple harmonic motion, then the number of cycles it completes in $66 \,s$ is

$A$ particle of mass $m$ is attached to three identical springs $A, B$ and $C$ each of force constant $k$ as shown in the figure. If the particle of mass $m$ is pushed slightly against the spring $A$ and released,then the time period of oscillations is

Find the maximum amplitude for safe $SHM$ (the block does not topple during $SHM$) of a cubical block of side $a$ on a smooth horizontal floor as shown in the figure (the spring is massless). The spring is attached at a height of $2a/3$ from the floor.

$A$ mass $m = 1.0\,kg$ is placed on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released,the mass executes simple harmonic motion. The spring constant is $k = 500\,N/m$. What is the amplitude $A$ of the motion,so that the mass $m$ tends to get detached from the pan? (Take $g = 10\,m/s^2$).

When a mass $m$ is attached to a spring,it oscillates with a period of $4 \, s$. When an additional mass of $2 \, kg$ is attached to the spring,the time period increases by $1 \, s$. The value of $m$ is ........... $kg$.

In the situation as shown in the figure,the time period of vertical oscillation of the block for small displacements will be: