Here's a complex physics problem for you, with a real world application. About a year ago, my mom was in a car accident that prevents her still from playing the harp as her profession. In order to return to work, however, her physical therapist needs to know how much force it takes to pull a harp string (sufficient enough force to produce sound) so that he can tell if she is ready to exert that amount of force regularly. One might think that this would be a fairly simple SHM problem, but it's not quite that easy. Here are the conditions:
Each string is a different length, and thus each would require a different amount of force to pull.
There are three different types of strings, and each type is made up of a different material
The harder each string is pulled, the louder the sound, so the force would have to be calculated back from the amount of sound produced, and then pumped through SHM (I think...)
To give you an idea, the combined tension of the all strings on the soundboard is approximately 2.5 TONS. We're dealing with some large forces here. What would you do to solve this problem, and what information would you need? A very real world application of everything we've learned. The challenge is out there. Now the task is solving it.