A weight of 200 g, suspended by a spring, vibrates at a frequency of 4 Hz.
| September 25, 2021 | education
A weight of 200 g, suspended by a spring, vibrates at a frequency of 4 Hz. With what frequency will a 50g load vibrate if it is suspended on the same spring?
The oscillation frequency of a spring pendulum can be calculated using the formula:
υ = 1 / 2Π * √ (k / m), where υ is the oscillation frequency of the pendulum (υ = 4 Hz), k is the stiffness of the spring (N / m), m is the mass of the load suspended from the spring (m = 200 g = 0 , 2 kg).
Let us express and calculate the stiffness of the spring:
k = (υ * 2Π) 2 * m = (4 * 2 * 3.14) 2 * 0.2 ≈ 126.2 N / m.
The oscillation frequency for the load is m1 = 50 g = 0.05 kg.
υ1 = 1 / 2Π * √ (k / m1) = 1 / (2 * 3.14) * √ (126.2 / 0.05) = 8 Hz.
Answer: The oscillation frequency will be 8 Hz.
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