A system of springs with their spring constants are as shown in figure. What is the frequency of oscillations of the mass m ?

Explanation

Here, `k_(3)` and `k_(4)` are in parallel and they together are in series with `k_(1)` and `k_(2)` . The effective spring constant of the system is
`(1)/(K)=(1)/(k_(1))+(1)/(k_(2))+(1)/((k_(3)+k_(4)))`
`=(k_(2)(k_(3)+k_(4))+k_(1)(k_(3)+k_(4))+k_(1)k_(2))/(k_(1)k_(2)(k_(3)+k_(4)))`
or `K=(k_(1)k_(2)(k_(3)+k_(4)))/((k_(1)+k_(2))(k_(3)+k_(4))+k_(1)k_(2))`
Frequency of oscillation,
`v=(1)/(2pi)sqrt((K)/(m))`
`=(1)/(2pi)sqrt((k_(1)k_(2)(k_(3)+k_(4)))/({(k_(1)+k_(2))(k_(3)+k_(4))+k_(1)k_(2)}m))`