A spring has spring constant k and l. If it cut into piece spring in the proportional to `alpha : beta : gamma` then obtain the spring constant of every piece in term of spring constant of original spring (Here, `alpha, beta " and "gamma` are integers).

Explanation

Suppose length of `alpha, beta" and "gamma" are "l_(1), l_(2)" and "l_(3)` respectively and total length `l= alpha+beta + gamma= l_(1), l_(2), l_(3)`
`therefore l_(1)=` spring constant of `alpha` length
`k_(1) = (kl)/(l_1)= (k(alpha+beta+gamma))/(alpha)`
` l_(2)=` spring constant of `beta` length
`k_(2) = (kl)/(l_2)= (k(alpha+beta+gamma))/(beta)`
and ` l_(3)=` spring constant of `gamma` length
`k_(3) = (kl)/(l_3)= (k(alpha+beta+gamma))/(gamma)`.