A mass $\mathrm{m}$ is suspended from a spring of negligible mass and the system oscillates with a frequency $f_1$. The frequency of oscillations if a mass $9 \mathrm{~m}$ is suspended from the same spring is $f_2$. The value of $\frac{f_1}{f_{.2}}$ is_____________.

Assuming all pulleys, springs and string massless. Consider all surface smooth. Choose the correct statement $(s)$

A mass of $0.2\,kg$ is attached to the lower end of a massless spring of force-constant $200\, N/m,$ the upper end of which is fixed to a rigid support. Which of the following statements is/are true ?

A mass $M$ is suspended by two springs of force constants $K_1$ and $K_2$ respectively as shown in the diagram. The total elongation (stretch) of the two springs is

In the figure shown, there is friction between the blocks $P$ and $Q$ but the contact between the block $Q$ and lower surface is frictionless. Initially the block $Q$ with block $P$ over it lies at $x=0$, with spring at its natural length. The block $Q$ is pulled to right and then released. As the spring - blocks system undergoes $S.H.M.$ with amplitude $A$, the block $P$ tends to slip over $Q . P$ is more likely to slip at

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