The oscillations represented by curve $1$ in the graph are expressed by equation $x=A\sin \omega t$ . The equation for the oscillations represented by curve $2$ is expressed as:

The coefficient of friction between block of mass $m$ and $2\mathrm{m}$ is $\mu =2\tan \left(\theta \right)$. There is no friction between a block of mass $2\mathrm{m}$ and inclined plane. The maximum amplitude of two block system for which there is no relative motion between both the blocks-

A constant force produces maximum velocity $v$ on the block connected to the spring of force constant $k$ as shown in the figure. When the force constant of spring becomes $4\mathrm{k},$ the maximum velocity of the block is (block is at rest when spring is relaxed):

A system is shown in the figure. The time period for small oscillations of the two blocks will be

A block of mass $\text{'}m\text{'}$ is attached with two springs of spring constant $\text{'}k\text{'}$ is performing $\mathrm{SHM}$ on a smooth horizontal surface. One of the spring is cut when the block is at the extreme position. Find the ratio of the amplitude of new $\mathrm{SHM}$ and old $\mathrm{SHM}.$

A block of mass $\text{'}m\text{'}$ is suspended from a spring and executes vertical $\mathrm{SHM}$ of time period $T$ as shown in figure. The amplitude of the $\mathrm{SHM}$ is $A$ and spring is never in compressed state during the oscillation. The magnitude of the minimum force exerted by spring on the block is