The oscillation frequency of the mathematical pendulum is 2.6 Hz.

| May 7, 2021 | education

The oscillation frequency of the mathematical pendulum is 2.6 Hz. What will be the oscillation frequency of the same pendulum if its length is increased by 69%?

To determine the value of the oscillation frequency of the presented pendulum, we apply the formula: νx = 1 / 2Π * √ (g / lx), whence we express: 1 / (4 * Π ^ 2) = g / (lx * νx ^ 2) and lx * νx ^ 2 = 1 / (g * 4 * Π ^ 2). Therefore, the equality will be true: l1 * ν1 ^ 2 = l2 * ν2 ^ 2 and ν ^ 2 = √ (l1 * ν1 ^ 2 / l ^ 2).

Variable values: l2 (final length of the pendulum) = 1.69l1 (initial length of the pendulum); ν1 – initial vibration frequency (ν1 = 2.6 Hz).

Calculation: ν2 = √ (l1 * ν1 ^ 2 / l ^ 2) = √ (l1 * 2.62 / 1.69l21) = 2 Hz.

Answer: After increasing the length of the presented pendulum, its oscillation frequency will be equal to 2 Hz.



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