What is the period of a simple pendulum 83 cm long on the Earth?
To find the period of a simple pendulum, we can use the formula:
T = 2π * √(L / g)
Where:
T = Period of the pendulum
L = Length of the pendulum
g = Acceleration due to gravity
In this case, the length of the pendulum is given as 83 cm. However, we need to convert it to meters because the formula requires the length to be in meters. Since 1 meter is equal to 100 centimeters, we can convert 83 cm to meters by dividing it by 100:
L = 83 cm / 100 = 0.83 m
The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Now we can substitute the values into the formula to calculate the period:
T = 2π * √(0.83 / 9.8)
Using a calculator or a mathematical software, we can evaluate the expression:
T ≈ 2π * √(0.0838775)
T ≈ 2π * 0.289223
T ≈ 1.8174458 seconds
Therefore, the period of a simple pendulum with a length of 83 cm on Earth is approximately 1.82 seconds.