Question

The length of time (T) in seconds it takes the pendulum of a clock to swing through one compete cycle is givenby the formulaT= 2T✔️L/32 Where L is the length, in feet, of the pendulum, and is pie approximately 22/7. How long must the pendulum be of one complete cycle takes 2 seconds? Answer as a fraction or round to at least 2 decimal places.The pendulum must be__ feet.

Answer 1

we have the formula

`T=2\pi\sqrt{(L)/(32)}`

For T=2 seconds

substitute in the given formula

`\begin{gathered} 2=2\pi\sqrt{(L)/(32)} \\ \\ 1=(22)/(7)\sqrt{(L)/(32)} \\ \\ squared\text{ both sides} \\ \\ ((7)/(22))^2=(L)/(32) \\ \\ L=(7^2*32)/(22^2) \\ \\ L=3.24\text{ ft} \end{gathered}`