The condition if the frictional force on block m2 is to act in the direction of its displacement from mean position.
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Solution
Suppose the system is displaced towards left by a distance x. Restoring force on m1: F=m1ω2x (towards right) =m1(k1+k2m1+m2)x Friction f on it will be towards right if, k1x<F or k1x<m1(k1+k2m1+m2)x or k1k2<m1m2