Two springs of force constants k and 2 k are connected to a mass as shown in figure. The frequency of oscillation of the mass is

Step-by-step solution

Let the mass m be displaced towards right by a distance x . Then the spring 1 will be extended and the spring 2 will be compressed by an amount of x each. The restoring force on mass m due to spring 1 is F₁=-k x And the restoring force due to spring 2 is F₂=-(2 k) x Total force on the mass m is aligned & F=F₁+F₂=-k x-2 k x=-3 k x & m d^2 x d t^2 =-3 k x d^2 x d t^2 + 3 k m x=0 & d^2 x d t^2 + ^2 x=0 where ^2= 3 k m = 3 k m & f= 2 = 1 2 3 k m . aligned