1. The problem statement, all variables and given/known data *according to my teacher, the problem can be solved either through differentials or quick algebra, but she prefers differentials as the answer in order for us to get used to Calculus, so that's the route I'd like to take it A pendulum made from a string and small metal ball swings back and forth. The formula for its period is given by the following: T = 2*pi*sqrt(L/g), where T is the period, pi is a constant, L is the length of the string and g is the gravitational force acting on it. In this situation, do not assume gravity is under the constant of 980 cm/s^2. Solve the following problems: A) Suppose the value of T is measured exactly (100%), but L is off by 1%. How much will g be off by? B) Suppose that the value of L is measured exactly (100%), but T is off by 1%. How much will g be off by? 2. Relevant equations T = 2*pi*sqrt(L/g) Chain Rule Product Rule Quotient Rule Power Rule 3. The attempt at a solution A) T = 2pi*(0.99L/g)^.5 T' = 2pi * .5 * (0.99L/g)^-.5 * [(0.99g-0.99Lg')/g^2] Then after lots of cancelling out: T' = [pi(g - Lg')]/Lg g' = [(LgT'/pi) - g] / -L B) 0.99T = 2pi*(0.99L/g)^.5 0.99 = [(pi)(gL'-Lg')] / Lg g' = -g[(0.99/pi) - (L'/L)] I have no idea if I did this right, or if I even answered my question correctly (since I don't even have a percentage... so I don't really know :/ ), so any help is appreciated, thank you!