The period, T, of a pendulum can be approximated by the formula β 2πβπΏπ, 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
.
The formula Tβ2πβπΏπ can be rearranged to solve for L:
L = (T / (2π))^2 * g
Substituting T = 2 s and g = 9.8 m/sΒ² gives:
L = (2 / (2π))^2 * 9.8 β 0.10 m
We can rearrange the formula for the period of a pendulum to solve for the length, L. The formula is T β 2πβπΏπ
Given that the period, T, is 2 seconds and the gravitational constant, g, is 9.8 m/s^2 on Earth, we can substitute these values into the formula:
2 β 2πβπΏ(9.8)
Dividing both sides of the equation by 2πβπΏ(9.8):
2/(2πβ(9.8)) β βπΏ
Squaring both sides of the equation:
(2/(2πβ(9.8)))^2 β L
Evaluating the expression on the left-hand side:
(2/(2πβ(9.8)))^2 β L
0.10162 β L
Therefore, the approximate length of the pendulum is 0.10162 meters.
To find the approximate length of the pendulum given its period of 2 seconds, we can rearrange the formula:
T β 2πβπΏπ
Let's substitute the known values:
2 β 2πβπΏ(9.8)
Next, we can simplify the equation by dividing both sides by 2π and then squaring both sides:
1 β (βπΏ(9.8))Β²
1 β 9.8πΏ
Now, we can solve for L by dividing both sides by 9.8:
1/9.8 β L
L β 0.102 meters (rounded to three decimal places)
Therefore, the approximate length of the pendulum is approximately 0.102 meters.