calculate the period and frequency of a 3.500 m long pendulum at the following locations:
a) the north pole, where acceleration due to gravity is 9.832 m/s^2
b) chicago, where acceleration due to gravity is 9.803 m/s^2
c) jakarta, indonesia, where acceleration due to gravity is 9.782 m/s^2
To calculate the period and frequency of a pendulum, we can use the formula:
T = 2π * √(L / g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
a) In the case of the North Pole, where acceleration due to gravity is 9.832 m/s^2 and the length of the pendulum is 3.500 m:
T = 2π * √(3.500 / 9.832)
T ≈ 2π * √0.3554
T ≈ 2π * 0.5963
T ≈ 3.750 seconds
The frequency, f, is the reciprocal of the period:
f = 1 / T
f = 1 / 3.750
f ≈ 0.2667 Hz (rounded to four decimal places)
b) In the case of Chicago, where acceleration due to gravity is 9.803 m/s^2 and the length of the pendulum is 3.500 m:
T = 2π * √(3.500 / 9.803)
T ≈ 2π * √0.3573
T ≈ 2π * 0.5977
T ≈ 3.760 seconds
f = 1 / T
f = 1 / 3.760
f ≈ 0.2657 Hz (rounded to four decimal places)
c) In the case of Jakarta, Indonesia, where acceleration due to gravity is 9.782 m/s^2 and the length of the pendulum is 3.500 m:
T = 2π * √(3.500 / 9.782)
T ≈ 2π * √0.3573
T ≈ 2π * 0.5972
T ≈ 3.749 seconds
f = 1 / T
f = 1 / 3.749
f ≈ 0.2668 Hz (rounded to four decimal places)
To calculate the period and frequency of a pendulum at different locations, we can use the formula:
T = 2π√(L/g)
Where:
T is the period of the pendulum,
L is the length of the pendulum, and
g is the acceleration due to gravity at that location.
To calculate the frequency, we can use the formula:
f = 1/T
Where:
f is the frequency of the pendulum.
Now, let's calculate the period and frequency at each location:
a) The North Pole (acceleration due to gravity = 9.832 m/s^2):
Using the given length, L = 3.500 m, and the acceleration due to gravity, g = 9.832 m/s^2, we can substitute the values into the formula:
T = 2π√(3.500/9.832)
T ≈ 6.299 seconds
To calculate the frequency, we use the formula:
f = 1/6.299
f ≈ 0.159 Hz
b) Chicago (acceleration due to gravity = 9.803 m/s^2):
Using the given length, L = 3.500 m, and the acceleration due to gravity, g = 9.803 m/s^2:
T = 2π√(3.500/9.803)
T ≈ 6.293 seconds
To calculate the frequency:
f = 1/6.293
f ≈ 0.159 Hz
c) Jakarta, Indonesia (acceleration due to gravity = 9.782 m/s^2):
Using the given length, L = 3.500 m, and the acceleration due to gravity, g = 9.782 m/s^2:
T = 2π√(3.500/9.782)
T ≈ 6.288 seconds
To calculate the frequency:
f = 1/6.288
f ≈ 0.159 Hz
Therefore, the period and frequency of the pendulum at each location are approximately:
a) The North Pole: Period = 6.299 seconds, Frequency = 0.159 Hz
b) Chicago: Period = 6.293 seconds, Frequency = 0.159 Hz
c) Jakarta, Indonesia: Period = 6.288 seconds, Frequency = 0.159 Hz