Consider a pendulum of length 4.720 m.
The acceleration of gravity is 9
.
832 m
/
s
2
.
a) What is its period at the North Pole?
Answer in units of s
009 (part 2 of 6) 10.0 points
b) What is its frequency?
Answer in units of Hz
a. T^2 = 4*pi^2(L/g).
L in meters.
g in m/s^2.
b. F = 1/T.
To find the period and frequency of a pendulum, we can use the following formulas:
1. Period (T) = 2π * √(L/g)
2. Frequency (f) = 1 / T
Where:
- L is the length of the pendulum
- g is the acceleration due to gravity
a) To find the period at the North Pole, we need to know the length of the pendulum (L) and the acceleration due to gravity (g).
Given:
- Length of the pendulum (L) = 4.720 m
- Acceleration due to gravity (g) = 9.832 m/s^2
Substituting the given values into the formula:
T = 2π * √(L/g)
T = 2 * 3.14159 * √(4.720 / 9.832)
T = 2 * 3.14159 * 0.48512
T ≈ 3.04005 s (rounded to five decimal places)
Therefore, the period of the pendulum at the North Pole is approximately 3.04005 seconds.
b) To find the frequency, we can use the formula:
f = 1 / T
Substituting the value of T calculated in part a):
f = 1 / 3.04005
f ≈ 0.32838 Hz (rounded to five decimal places)
Therefore, the frequency of the pendulum at the North Pole is approximately 0.32838 Hz.