Consider a pendulum of length 4.557 m. The acceleration of gravity is 9.832 m/s2 .

a) What is its period at the North Pole? Answer in units of s.

b) What is its frequency? Answer in units of Hz.

c) What is its period in Chicago, where g = 9.803 m/s2? Answer in units of s.

d) What is its frequency? Answer in units of Hz.

e) What is its period in Jakarta, Indonesia, where g = 9.782 m/s2? Answer in units of s.

f) What is its frequency? Answer in units of Hz.

My teacher didn't specify if 9.821 m/s^2 is the value of the North Pole. We don't have class this week because of Spring Break and it's due the morning we get back, so I can't ask him any questions. But I got C through F now, thank you!

To calculate the period and frequency of a pendulum in different locations, 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

a) To find the period at the North Pole, where g = 9.832 m/s^2:

T = 2π√(4.557 / 9.832)
T ≈ 4.564 s

b) To find the frequency, we can use the formula: f = 1/T

f = 1 / 4.564
f ≈ 0.219 Hz

c) To find the period in Chicago, where g = 9.803 m/s^2:

T = 2π√(4.557 / 9.803)
T ≈ 4.568 s

d) To find the frequency:

f = 1 / 4.568
f ≈ 0.219 Hz

e) To find the period in Jakarta, where g = 9.782 m/s^2:

T = 2π√(4.557 / 9.782)
T ≈ 4.572 s

f) To find the frequency:

f = 1 / 4.572
f ≈ 0.219 Hz

To solve this problem, we need to use the equations for the period and frequency of a pendulum. The period (T) is the time it takes for the pendulum to complete one full swing, and the frequency (f) is the number of complete swings per second.

The equation for the period of a pendulum is given by:
T = 2π * √(L/g)

where L is the length of the pendulum and g is the acceleration due to gravity.

The equation for the frequency of a pendulum is:
f = 1/T

a) To find the period at the North Pole:
L = 4.557 m
g = 9.832 m/s² (acceleration due to gravity)

Substituting these values into the equation for the period:
T = 2π * √(4.557/9.832)

Calculating this expression gives us the period at the North Pole.

b) To find the frequency:
We can use the equation:
f = 1/T

Substituting the value of T we found in part a, we can calculate the frequency.

c) To find the period in Chicago:
L = 4.557 m
g = 9.803 m/s²

Using the same formula as in part a, we can substitute these values and calculate the period in Chicago.

d) To find the frequency:
Using the same formula as in part b, substitute the value of T found in part c to calculate the frequency in Chicago.

e) To find the period in Jakarta:
L = 4.557 m
g = 9.782 m/s²

Again, using the same formula as in part a, substitute these values and calculate the period in Jakarta.

f) To find the frequency:
Using the same formula as in part b, substitute the value of T found in part e to calculate the frequency in Jakarta.

Is 9.832 m/s^2 the value at the North Pole? You should have made that clear.

Formulas to use are:

Period: P = 2 pi sqrt(L/g)

frequency: f = 1/P

You do the numbers.