If the length of the pendulum thread is reduced by 4 times, how will the period and frequency of oscillations change?
| March 12, 2021 | education
The oscillation period of the mathematical pendulum:
T = 2Π * √ (l / g), where l is the length of the mathematical pendulum, g is the acceleration of gravity.
T1 = 2Π * √ (l1 / g).
T2 = 2Π * √ (l2 / g), where l2 = 1/4 l1.
T2 / T1 = 2Π * √ (1/4 l1 / g) / 2Π * √ (l1 / g) = 1/2.
Oscillation frequency:
ώ = √ (g / l).
ώ1 = √ (g / l1).
ώ2 = √ (g / l2), where l2 = 1/4 l1.
ώ2 / ώ1 = √ (g / 1/4 l1) / √ (g / l1) = 2.
Answer: The oscillation period of the pendulum will decrease by 2 times, the oscillation frequency of the pendulum will increase by 2 times.
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