If a spring has time period T, and is cut into (n) equal parts, then the time period of each part will be.

Explanation

Let k be the spring constant of a given spring.
Then `T=2pisqrt((m)/(k))`
When spring is cut into n parts, let `k^(')` be the spring constant of each part. Then
`(1)/(k)=(1)/(k^('))+(1)/(k^('))+...n`term `=(n)/(k^('))or k^(')=nk`
New time period of oscillation is
`T^(')=2pisqrt((m)/(k^(')))=2pisqrt((m)/(nk))=(T)/(sqrt(n))`