One body is suspended from a spring of length ‘l’, spring constant ‘k’ and has time period T. Now if a spring is divided in two equal parts which are joined in parallel and the same body is suspended from this arrangement then determine new time period.

now k is inversly proportional to length ..

so ,      K₂/K₁   = L₁/L₂                          

from here we can compare force constant of two different lengths of  wire of same material..

let force constant of each half is k¹ after cutting then

k¹/k = L/(L/2)

k¹ = 2k

both of these parts are connected parallel so net force constant = 2k+2k=4k

I thnk now you can solve.

Regards

Arun (askIITians forum expert)