Second Degree Taylor Polynomial?

Imagine a swinging pendulum. The function f(t) will give the angle this pendulum makes with a vertical line at time t. Arguments from physics show that this function must satisfy the following equation for all t: f^2 (t) + k sin(f(t)) = 0 where k is a constant calculated from the length of the pendulum and from gravity. a. Find the second degree Taylor polynomial for sin(t) centered at 0. b. Explain why this Taylor polynomial implies that any function which satises: f^2(t) + kf(t) = 0 is a good approximation for modelling the movement of a pendulum (provided that f(t) remains small). c. Find a function which satisies: f^2(t) + kf(t) = 0 then graph its behavior over time. Explain why this function approximates the motion of a pendulum.