The period, T, of a pendulum can be approximated by the formula ā 2šāšæ/š, where L is the length of the pendulum and g is the gravitational constant. What is the approximate length of the pendulum if it has a period of 2 s? Note: On Earth the gravitational constant is 9.8 m/s2
To find the approximate length of the pendulum, we can rearrange the formula for the period and solve for L:
T ā 2šāšæ/š
Given that the period T is 2 seconds and the gravitational constant g is 9.8 m/s^2, we can substitute these values into the formula:
2 ā 2šāšæ/9.8
Next, we can simplify the equation by dividing both sides by 2:
1 ā šāšæ/9.8
Multiply both sides by 9.8 to isolate the square root of L:
9.8 ā šāšæ
Then divide both sides by š to obtain the length of the pendulum L:
9.8/š ā āšæ
To solve for L, we square both sides:
(9.8/š)^2 ā šæ
Using a calculator, we can evaluate the left side of the equation:
(9.8/š)^2 ā 9.9342
Therefore, the approximate length of the pendulum is 9.9342 meters.