Question

The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be ___________

(a) T/4

(b) T

(c) T/2

(d) 2T

I have been asked this question in class test.

My query is from Wave Motion in portion Waves of Engineering Physics I

Answer 1

Right option is (c) T/2

To explain: T=2π√(m/k), k=F/x

When the spring is cut into four equal parts,

k^‘=F/(x/4)=4(F/x)=4k

T^‘=2π√(m/k^‘)=2π√(m/4k)=T/2.