The length of the first mathematical pendulum is 4 times the length of the second mathematical pendulum.
| August 17, 2021 | education
The length of the first mathematical pendulum is 4 times the length of the second mathematical pendulum. Find the ratio of the oscillation frequency of the second pendulum to the oscillation frequency of the first.
The oscillation frequency of the first mathematical pendulum:
ν1 = 1 / 2Π * √ (g / l1), where g is the acceleration of gravity, l1 is the length of the first pendulum.
Oscillation frequency of the second pendulum:
ν2 = 1 / 2Π * √ (g / l2), where g is the acceleration of gravity, l2 is the length of the first pendulum (according to the problem statement, l1 = 4l2).
ν1 = 1 / 2Π * √ (g / 4l2) = 1/2 Π * √ (g / l2) * 1/2
Pendulum frequency ratio:
ν2 / ν1 = (1/2 Π * √ (g / l1)) / (1 / 2Π * √ (g / l1) * 1/2) = 1 / 1/2 = 2.
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