Write short notes on two springs connected in parallel.

Explanation

Let us consider only two springs of springs constants, `k_(1) and k_(2)` atttached to a mass m as shown in Figure.

Net force for the displacement of mass m is
`F=-k_(p)x " "....(1)`
where `k_(p)` is called effective spring constant. Let the first spring be elongated by a displacement x due to foce `F_(1)` and second spring be elongated by the same displacement x due to force `F_(2)` then the net force
`F=-k_(1)x-k_(2)x " "....(2)`
Equating equations (2) and (1) we get
`k_(p)=k_(1)+k_(2) " "....(3)`
Generalizing for n springs connected in parallel,
`k_(p)overset(n) underset(i=1)sum k_(1) " "...(4)`
If all spring constants are indentical i.e., `k_(1)=k_(2)=...k_(n)=k` then
`k_(p)=nk " "....(5)`
It is implied that the effective spring constant increaes by a factor n. so for the springs in parallel connection, the effective spring constant is greater than individual spring constant.