Question

A block of mass `m_(1)=1kg` is attached to a spring of force constant `k=24N//cm` at one end and attached to a string tensioned by mass `m_(2)=5kg` . Dedcue the frequency of oscillaitons of the system. If `m_(2)` is initially supported in hand and then suddenly released, find

`(a)` instantaneous tension just after `m_(2)` is released . ltbr. `(b)` the maximum displacement of `m_(1)`.
`(c)` the maximum and minimum tensions in the string during oscillations.

Answer 1

Correct Answer - A::B::C
`T=2pisqrt((m_(1)+m_(2))/(K))`
`=2pi sqrt((6)/(2400))=(pi)/(10)`
`rArr f=(10)/(pi)`
Instantaneous tension just after `m_(2)` is released will be zero as the spring is unstressed.
Amplitude of `m_(1)=m_(2)g//K=25//12 cm`, hence maximum displacement of `m_(1) ` will be `25//6 cm`.