A simple harmonic oscillator consist 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. `T//2`
B. `(T)/(sqrt(2))`
C. `sqrt(2)T`
D. 2T

Answer

B

Explanation

`T=2pisqrt((m)/(k))`
If the spring is cut into two equal parts, the force constant of each part becomes 2k. Therefore,
`T.=2pisqrt((m)/(2k))=(T)/(sqrt(2))`