Question

The pendulum of an antique clock has been damaged and needs to be replaced. If the original pendulum completed one swing every 0.7 seconds, how long should the new pendulum be?

Answer 1

Answer: the correct answer is 12 centimeters.

Step-by-step explanation:

Answer 2

Use the pendulum equation:
$T = 2 \pi \sqrt{\frac{L}{g}}$
where L is length of pendulum, g is acceleration of gravity
T is period or length of time to complete 2 swings (1 cycle)

Given 0.7s to complete 1 swing, then the period is 1.4 s.
Solve for L
 $2 \pi \sqrt{\frac{L}{g}}= 1.4 \\ \\ \sqrt{\frac{L}{g}} = \frac{0.7}{\pi} \\ \\ \frac{L}{g} = \frac{(0.7)^2}{\pi^2} \\ \\ L = 9.8(\frac{0.7}{\pi})^2 = 0.4865$

The length of new pendulum is about 0.48 meters