The period of a simple pendulum of length $L$ feet is given by $$T=2\pi \sqrt{\frac{L}{g}} \hbox{~seconds.}$$ We assume that $g$, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is that of a clock that keeps good time when $L = 4$ feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at $L=4$ feet.)
Your answer: seconds.