Project #491 - Combined Function Task

I am having trouble with a combined function task. It is a mass that is attached to a spring, and a spring to a wall (think, a doorstop). When it is pulled away from the wall it oscillates along the floor, however due to friction on the floor it slows down as it approaches 0. Along the lines of a dampened sine wave. The function we need is: d(t) = f (t)× g(t) + r It follows the following parameters: • The mass is at a resting position of r = 30 cm. • The spring provides a period of 2 s for the oscillations. • The mass is pulled to d = 50 cm and released. • After 10 s, the spring is at d = 33 cm. I started with the equation for the model without friction (so as though it remained constant) and I believe it would be something like 20*cos(3x)+30 (feel free to correct me if I'm wrong). From this point, however, I am not sure how to determine the function when the friction is applied. And, I'm not sure where to go from here. I really just need the two functions, first off is 20*cos(3x)+30 correct to model this data if no friction is involved? And second, when we need to calculate the impact of friction what is the new function? You can simply email it to me in whatever format you like, it's not an exam or essay I need (not looking for anyone to write an assignment for me), I just need help with coming up with the function. :)

Subject Mathematics
Due By (Pacific Time) 06/05/2012 12:00 am
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