Repeat the previous exercise if the angle between each pair of springs is `120^@` initially.

Answer

`Time period =T=(2pi)/omega=2pisqrt((2m)/(3k))`

Explanation

In this case if the particle m is pushed against C a by distance x. total resultant force acting on man m is given by
`F=kx+(kx)/2=(3kx)/2`
[Because net force by A and B ]
` sqrt((kx/2)^2+(kx/2)^2+2(kx/2)(kx/2)) cos120^@`
`=kx/2`
` :. a=F/m=(2kx)/(2m)`
`rarr a/x=(3k)/(2m)=w^2`
`rarr omega=sqrt(3k)/(2m)`
`:. Time period =T=(2pi)/omega=2pisqrt((2m)/(3k))`