The time periods for vertical harmonic oscillations of the three systems of single, two series spring and two parallel springs, each springs have a force constant 'k'. The ratio of time periods of the system is

Options

A. `(1)/(sqrt(2)):sqrt(2):1`
B. `sqrt(2):1:(1)/(sqrt(2))`
C. `1:sqrt(2):(1)/(sqrt(2))`
D. `1:(1)/(sqrt(2)):sqrt(2)`

Answer

C

Explanation

The period of single spring
`T_(1)=2pisqrt((m)/(k))`
Period of two springs in series
`T_(2)=2pisqrt((2m)/(k))`
Period of two springs in parallel
`T_(3)=2pisqrt((m)/(2k))` ltbr. `T_(1):T_(2):T_(3)=1:sqrt(2):(1)/(sqrt(2))`