A particle of mass 'm' is attached to three identical springs `A,B` and `C` each of force constant 'K' as shown in figure. If the particle of mass 'm' is pushed slightly against the spring 'A' and released the period of oscillations is

Options

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

Answer

B

Explanation

Total restoring force on the mass along OA-
`F_("net")=F_(A)+F_(B)cos45^(@)+F_(C)cos45^(@)`
`=ky+2ky.cos45^(@)`.

`implies F_("net")=ke+2k(ycos45^(@))cos45^(@)=2ky`
`implies F_("net")=k.y`
`therefore k.=2k," "T=2pisqrt((m)/(k.))=2pisqrt((m)/(2k))`.