Write short notes on two springs connected in series.

Explanation

Let us consider two springs whose spring constant are `k_(1) and k_(2)` and which are connected to a mass m as shown in Figure.

Let F be the applied force towards right as shown in figure. The net displacement of the mass point is
`x=x_(1)+x_(2)`
from Hooke's law, the net force,
`F=-k_(s)(x_(1)+x_(2))`
The effective spring can be calculated as
`-(F)/(k_(1))-(F)/(k_(2))=-(F)/(k_(s))`
`(1)/(k_(s))=(1)/(k_(1))+(1)/(k_(2))`
(or)
When n springs connceted in series, the effective spering constant in series is
`(1)/(k_(s))=(1)/(k_(1))+(1)/(k_(2))+(1)/(k_(3))+....+(1)/(k_(n))`
`overset(n) underset(i=1)sum(1)/(k_(i))`
If all spring constants are indenitcal i.e., `k_(1)=k_(2)=....=k_(n)=k` then
`(1)/(k_(s))=(n)/(k) rArr k_(s)=(k)/(n)`
Theis means that the effective spring constant reduces by the factor n. so for, springs in series connection, the effective spring constant is lesser than the individual spring constants.