The time period of a body suspended from a spring is T. What will be the new time period, if the spring is cut into the two equal parts and (i) the mass is suspended from one part? (ii) the mass is suspended simultaneously from both the parts?

Explanation

Tiem period of spring, `T=2pisqrt(m/K)`
When a spring is cut into two equal parts force constant of each part `K_(1)=2K`
i) For one piece, `T=2pisqrt(m/K_(1))=2pisqrt(m/K)(1)/(sqrt2)=(T)/(sqrt2)`

ii) When mass is suspended simultaneously from two parts `rArr` they are conncted in parallel. For springs in parallel `K_(p)=K_(1)+K_(2)=4K`
Time period, `T=sqrt(m/K_(p))=2pisqrt((m)/(4.K))=2pisqrt((m)/(K)(1)/(2)=(T)/(2)`