Question

which countries on both sides of the Atlantic experienced revolutions during the late 18th and early 19th centuries?

Answer 1

The both sides of the Atlantic are America and Europe.

In Europe, there was  a French revolution at the end of the 18th century. in 1848 many countries experienced revolution, for example Austria, German States, Italian States and Poland

In America there was the American Revolution in the US at the end of the 18th century. There were also similar revolutions in Latin American Countries in the 19th century, but they're usually called "war of Independence", not revolution.