How will the period of the filament pendulum change if its length is reduced by 9 times?
| September 19, 2021 | education
The oscillation period of the pendulum in the first case
T1 = 2p * √ (L1 / g),
in the second
T2 = 2p * √ (L2 / g).
Substitute the length ratio
L1 = 9 * L2;
T1 = 2p * √ (9 * L2 / g).
Find the ratio of periods
T1 / T2 = (2p * √ (9 * L2 / g)) / (2p * √ (L2 / g)) =
= √ ((9 * L2 / g) / (L2 / g)) = √9 = 3.
Answer: the period will change 3 times.
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