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_____________.

A block of mass $m$ attached to massless spring is performing oscillatory motion of amplitude $'A'$ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $fA.$ The value of $f$ is

If a vertical mass spring system is taken to the moon, will its time period after ?

A spring having a spring constant $‘K’$ is loaded with a mass $‘m’$. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is

A mass of $2\,kg$ is attached to the spring of spring constant $50 \,Nm^{-1}$. The block is pulled to a distance of $5 \,cm $ from its equilibrium position at $x= 0$ on a horizontal frictionless surface from rest at $t = 0$. Write the expression for its displacement at anytime $t$.