Here are some examples:
* He shook his head vigorously. (He shook his head with strong, energetic movements.)
* The team practiced vigorously for the upcoming game. (They practiced with a lot of effort and intensity.)
* She argued vigorously against the new policy. (She argued with passion and determination.)
The word "vigorously" can also be used to describe things that are growing or flourishing with great force and vitality.
* The plants in the garden grew vigorously in the warm weather.
* The economy is showing signs of vigorous growth.
Note: "Vigorously" is an adverb, so it modifies a verb.