A particle of mass m is attached to three springs A, B and C of equal force constant k as shown in figure. The angle between each pair of springs is 120° initially. If the particle is pushed slightly against the spring C and released, find the time period of oscillation.

Dear Abhishek

 

Given that the angle between any 2 spring is 120 than we can assume othere 2 also to be 120.Now let us take one spring on x axis then the othere 2 will make 60 degrees on the right .each has a constant k .so the right side 2 springs can be replaced by one spring as 2kcos60=k. We know that T=2 π/ω.   ω=√k’ / m . Now as we have replaced the 2 springs with a equivalent spring of k it become a linear system .so K’= 2k now substitute this in formula and then in the Time period formula. you will get T=2π √m/2k.