Question

a spring of force constant 'k' is cut into 2 parts whose lengths are in the ratio 1:2.The 2 parts are now connected in parallel and a block of mass 'm' is suspended at the end of the combined spring.find the period of oscillation performed by the block

Answer 1

Spring constant is inversely proportional to spring length. The original spring constant k becomes two springs with constants k1 = 3k and k2 = 3k/2, in parallel.

The effective spring constant of springs in parallel is obtaned by adding the separate spring constants; so the new spring constant becomes
k' = k1 + k2 = 9k/2.

The new period of oscillation is:

P = 2*pi*sqrt(m/k')
= 2*pi*sqrt(2/9)*sqrt(m/k)
= (2/3)*pi*sqrt(2m/k)

Answer 2

how is k1=3k and k2=3k/2.i am getting it as k/3 and 2k/3