The two spring pendulums have springs with an elasticity ratio (k1 / k2 = 4). The ratio of the mass of the goods (m1 / m2 = 1). What will be the ratio of the oscillation periods?
The oscillation period of the spring pendulum:
T = 2Π * √ (m / k), where m is the mass of the suspended load, k is the spring stiffness of the pendulum.
From the ratio: k1 / k2 = 4; k1 = 4k2; m1 / m2 = 1; m1 = m2.
First spring pendulum:
T1 = 2Π * √ (m1 / k1) = 2Π * √ (m2 / 4k2).
Second spring pendulum:
T2 = 2Π * √ (m2 / k2).
The ratio of the periods of fluctuations:
Т1 / Т2 = 2Π * √ (m2 / 4k2) / 2Π * √ (m2 / k2) = 1/2 * 2Π * √ (m2 / k2) / 2Π * √ (m2 / k2) = 1/2.
Answer: The ratio of the periods of oscillations T1 / T2 = 1/2.
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