how did the united states respond when north vietnam attacked a us warship and sent troops to south vietnam in the early 1960s?

Congress authorized the president to escalate the conflict.

Explanation:

This incident is known as the Gulf of Tonkin incident and it resulted in the Gulf of Tonkin Resolution. The incident happened when North Vietnamese warships attacked US warships in the Gulf of Tonkin. After the incident President Lyndon Johnson asked the congressional authorization to escalate the conflict, the authorization was called the Gulf of Tonkin Resolution.

The Unites States thought that the action was severe enough to declare war on north Vietnam.