A particle of mass m is attached to three springs A, B and C of equal force constant as shown in figure (12-E6). If the particle is pushed slightly against the spring C
and released, find the time period of oscillation.
Suppose the particle is pushed slightly against the spring C through displacement x.
Total resultant force on the particle is 
due to spring and 
due to spring A and B, is given by
Note: When the body pushed against C, the spring C tries to pull the block towards XL. At that moment the spring A and B tries to pull the block with force 
and 
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.
1