now its time for me to explain why the frequency of the second case cannot be derived for the second case both the forces exerted by the other two elements do not compensate each other. their horizontol components gets cancelled while their vertical components are in the same direction and hence they push it away and as there is no restoring force to keep it in shm the particle just pushed away but not set into shm
hence it has no frequency
please have mercy on me if i were wrong and correct me