"the pendulum of government authority has swung" over the lifetime of the american government.

The correct answer is between state and national governments.

This phrase refers to the power/authority that each branch of government possess. Throughout American history, the state and national governments have fought over which branch of government has the authority to make certain decisions. These decisions range from integration of black and white students during the 1950s to how to spend money from the federal government that is given to states. These are just a couple of issues that the state and national government fight over.