You are writing an essay which, I assume, makes the case that music has the power to change a person's mood, both positively and negatively. When you are making an argument for something (which is exactly what persuasion is--trying to convince someone that your position is the best one), your primary goal is to win your audience (readers) to your position. The best place to start is by winning them over in your introduction.
An introduction serves three general purposes in any any essay: it captures the readers' attention, it sets the tone (i.e., humorous, persuasive) for the essay, and it introduces the key points which will be addressed (thesis/purpose statement). The most effective attention-getting device for a persuasive essay is one which begins to get your readers to agree with your position by giving them something with which they will probably agree.
Since music is evocative (makes us thinks of times, places, people, smells, emotions), perhaps you can ask your readers to think of a time when, for example, they hear a song and it reminds them of something in their past. This is a common experience and proves that music has the power to "transport" us, so to speak, to another time and place.
Another possible attention-getting device might be a little "walk" through the places where we encounter music in our lives: churches, cars, restaurants, recitals, dances, even elevators. Each place has a different kind of music, designed to set a certain mood. A deejay at a dance is not likely to play hymns, for example, because they would be too serious or somber for a celebratory occasion. Your readers are likely to understand and agree with you about this, and you have established the premise that music has the power to create, affect, or change peoples' moods.
Music appeals to the senses, so perhaps an analogy to another sense might be effective to capture your readers' attention and make your point at the same time. Take whatever smell is meaningful to you--grandmother's baking, a smoky bonfire, a cinnamon-y apple pie on a fall day--and ask your readers to do the same. Just as we are transported to another time and place by familiar smells, we can be moved by music which is evocative (which reminds us) of other times and places.
What about finding a song whose lyrics might cause your readers to react by changing their mood, even just a little. That would certainly prove your point from the very beginning of your paper. I would not suggest being inflammatory or trying to shock, as then your point will be secondary to their reaction to such outrageousness. I am always moved to stand a little taller and even get a little weepy every time I hear--really hear--the national anthem or even "The Battle Hymn of the Republic," for example. No doubt you can think of something more contemporary and relevant to your audience.
Of course there is always the more standard (but still perfectly acceptable and effective) approach of using a quote, saying, or story to introduce your subject and capture your readers' attention. For example, in I Samuel 16:14-23, King Saul is distraught (troubled by an evil spirit), and the young shepherd David is able to soothe him with music. A play entitled A Mourning Bride by William Congreve contains these famous lines:
Musick has Charms to sooth a savage Breast,
To soften Rocks, or bend a knotted Oak.
Whatever you choose to do, be certain it is directly relevant/connected to your paper's thesis.