1) If you pluck a guitar string, pulling it to a height of A and letting go, we can model its motion as f(t) = A cos(t), where t is in milliseconds and A is a constant. a. The derivative tells you how...

Extracted text: 1) If you pluck a guitar string, pulling it to a height of A and letting go, we can model its motion as f(t) = A cos(t), where t is in milliseconds and A is a constant. a. The derivative tells you how fast the string is moving, and thus how loud the sound will be. Find the derivative. b. The faster it moves (bigger derivative), the louder it will be. What is the relationship between how far you pluck the string, A, and how loud it is? c. What is wrong with our model as t gets big (as compared to what you expect from a real guitar string).