Ask Mr. Smarty Plants

First, I think you need to define what you mean by "faster".  For instance, plants growing in very low light tend to become very tall, but it isn't because they are increasing their cell number.  Instead, their cells are elongating without dividing in an attempt to find light to carry out photosynthesis.  Photosynthesis is how plants convert the energy of the sun into food for growth.  See the answer to a previous question: "Why do plants grow faster in the dark?" So, it seems to me you need to decide for your experiment what measure you will use to determine growth.  Will you use plant height, number of leaves, size of the leaves?

Visible light is one of the forms of electromagnetic radiation that we receive from the sun.  We measure electromagnetic radiation in 'wavelengths' and the units we use are nanometers (nm). A nanometer is very small—one billionth of a meter, or one millionth of a millimeter.  We see the different wavelengths in visible light as colors. For instance, the wavelenths around 475 nm gives us blue light, those around 510 nm gives us green, and near 650 nm is red.  Plants don't use the entire spectrum of light for photosynthesis, they absorb light at two wavelengths to use in photosynthesis—430 nm, at the blue/violet end of visible light, and 662 nm at the far end of red.  You can read about the light spectrum and photosynthesis.   Natural light from the sun, of course, contains these wavelengths, so you expect—all other factors being equal—that plants would grow very efficiently in natural light. 

Synthetic light does not necessarily carry all wavelengths of light, different synthetic light sources produce different spectra.  You can see graphs of spectra from different light sources in a paper about how light wavelength and intensity affect poultry performance. However, there are lights made especially to produce light at the wavelengths that are used for photosynthesis.  You can find thousands of entries about such lights by googling "plant grow lights."  These "grow lights" should also be very effective in making plants grow.  There is, however, another aspect to the question of light that you will need to consider for your experiment—that is its intensity or how strong it is.  As you might expect, natural sunlight is much more intense than any light produced by an artificial source. More intensity means more energy transferred to the plant.  You may find that you will need to compensate by leaving your plants under the "grow lights" for a longer period than your plants growing under natural sunlight experience in the sun. You can find a very good discussion about light intensity and wavelength of "grow lights" compared to natural light in Fluorescent Plant Lighting. This article should also give you some ideas about how to set up your experiment so that you can answer the question you asked Mr. Smarty Plants:  "Will plants grow faster in natural light or artificial light or a combination of both?"