A particle of mass `m` is attached with three springs `A,B` and `C` of equal force constancts `k` as shown in figure. The particle is pushed slightly against the spring `C` and released. Find the time period of oscillation.
.

Answer

`=2pisqrt(m/(2k))`

Explanation

`a`. Suppose the particle is pushed lightly against the spring C through displacement x.
Total resultat force on the particle ils kx.
Due to spring C and `(kx)/2` due to spring A and B.
`:.` Total Resultant force
`=kx+sqrt((kx)^2/(sqrt2)^2)+(kx)^2/(sqrt2)^2`
Acceleration `=(2kx)/m`
`Time period =2pisqrt((displacement)/((Ac cel eration))`
`=2pisqrt(x/(2kx/m))`
`=2pisqrt(m/(2k))`
[Cause: When the body pushed against C the spring C tries to pulll the block XL. At that moment the spring A and B tries to pull the block with force `(kx)/sqrt2 and (kx)/sqrt2` respectively towards xy and xz respectively. So the total force on the block is due to the spring force C as well as the component of two spring force A and B.