Oscillation

A block of mass $m$  attached to a 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:

A particle executes S.H.M. with amplitude 'a' and time period 'T'. The displacement of the particle when its speed is half of maximum speed is   $\frac{\sqrt[]{x}a}{2}.$ The value of x is…………

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as $U=\frac{\alpha }{r^{10}}-\frac{\beta }{r^5}-3$

Where, and are positive constants. The equilibrium between two atoms will be ${\left(\frac{2\alpha }{\beta }\right)}^{\frac{a}{b}},$ ${\frac{}{}}^{\frac{}{}}$ where a =…………….