The string the spring and the puley shown in figure are light. Find the time period of the mass m.

Answer

`2pi sqrt(m/k)`

Explanation

When only m is hanging let the extention in the spring be l
So, `T_1=kl=mg`
When a force F is applied let the further extension be x
`:. T_2-k(x+l)`
`:.` Driving force =`T_2-T_1=k(x+l)-kl`
`=Kx`
:. Acceleration =`(Kx)/m`
`T=2pisqrt(x/a)`
`=2pisqrt(x/(kx/m))=2pi sqrt(m/k)`