A mass m is suspended from a spring of force constant k and just touches another identical spring fixed to the floor as shown in the fig. The time period of small oscillations is

Options

A. `2pisqrt((m)/(k))`
B. `pisqrt((m)/(k))+pisqrt((m)/((k)/(2)))`
C. `pisqrt((m)/((3k)/(2)))`
D. `pisqrt((m)/(k))+pisqrt((m)/(2k))`

Answer

D

Explanation

When the spring undergoes displacement in the downward direction it completes one-half oscillation while it completes another half oscillation in the upward direction. The total time period is
`T=pisqrt((m)/(k))+pisqrt((m)/(2k))`