Nitrogen is a limiting factor of growth. In your design of your experiment it would be good to take into account that plants demand different nutrients at different stages. Giving nitrogen to any plant near the point of maturity usually means less flowering and fruit and the production of green at the expense of fruit or flowering.
However, if you want to see the effect on growth then plant two plants of the same age under the same conditions. The plants should be young but have their first true leaves and about the same size. Then do the experiment measure the change in growth before and after and graph the growth in weeks. If you want to know how fast nitrogen can correct deficiencies, then start with a plant that is nitrogen deficient - you can measure the plant tissue nitrogen which would be the most empirically correct. But if you know a plant is nitrogen deficient (yellow leaves on the bottom, pale green leaves on the top), you can feed the plant nitrogen. How much depends on the size of the plant and document how long it takes to see a change.
A third experiment can be done if you use different kinds of nitrogen. Starting with same sized plants in similar conditions and same soil. Give one organic nitrogen and the other give it synthetic nitrogen and compare the growth rates. Use a fast growing plant like corn, if you want to see a measurable change in growth. If you use a slow growing plant, it may take a while longer.
Another thing about nitrogen is that is does not hang around for very long, so usually it needs to be given in divided doses.