Thread: linear approximation and the derivative...

Writing g for the acceleration due to gravity, the period, T, of a pendulum of length is given by the following equation.


(a) Show that if the length of the pendulum changes by , the change in the period, T, is given by the following equation. (Do this on paper. Your teacher may ask you to turn in this work.)

(b) If the length of the pendulum increases by 4%, by what percent does the period change?


ok i just need to be directed in the right path....need some help on how and where to start for this problem...any help is greatly appreciated...

mathaction

Originally Posted by mathaction

Writing g for the acceleration due to gravity, the period, T, of a pendulum of length is given by the following equation.


(a) Show that if the length of the pendulum changes by , the change in the period, T, is given by the following equation. (Do this on paper. Your teacher may ask you to turn in this work.)

(b) If the length of the pendulum increases by 4%, by what percent does the period change?


ok i just need to be directed in the right path....need some help on how and where to start for this problem...any help is greatly appreciated...

mathaction

Taylor's theorem to a first order approximation says that

where the derivative is taken with respect to l. This only works if is small. (Typically that means that is only a few percent of the size of l.)

Work this out and then define .

-Dan