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

Options

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

Answer

C

Explanation

The time period of oscillation,`T=2pisqrt(m/k)`
`k=alpha1/l`
`k^1=2k`(As the spring is cut into two parts)
`therefore T^1=2pisqrt(m/(2k))=1/sqrt(2)2pisqrt(m/k)=1/sqrt(2)=T`