A simple harmonic oscillator consists of a particle of mass m and an ideal spring with spring constant k. The particle oscillates with a time period T. The spring is cut into two equal parts. If one part oscillates with the same particle, the time period will be

Options

A. `2T`
B. `sqrt(2)T`
C. `(T)/(sqrt(2))`
D. `(T)/(2)`

Answer

C

Explanation

Mass of the particles = m and spring constant = k
The time period of oscillator, `T = 2 pi sqrt((m)/(k))`
As `k prop (1)/(I)" "("where, I is the length of the spring")`
`because" "k'=2k`
`therefore" "T' = 2pi sqrt((m)/(2k))=(1)/(sqrt(2))T=(T)/(sqrt(2))`