The two spring-mass system, shown in the figure, oscillates with a period T. If only one spring is used, the time period will be

Options

A. `T/sqrt2`
B. `T/2`
C. `sqrt2T`
D. `2T`

Answer

A

Explanation

Springs in series, `k_(eq)=(k*k)/(k+k)=k/2`
`T=2pisqrt((m)/(k_(eq)))=2pisqrt((m)/(k//2))=2pisqrt((2m)/(k))`
`T^'=2pisqrt(m/k)`
`T^'/T=1/sqrt2impliesT^'=T/sqrt2`