The cyclic oscillation frequency of a spring pendulum n = 2.5 times the cyclic oscillation frequency of a mathematical

| February 21, 2021 | education

The cyclic oscillation frequency of a spring pendulum n = 2.5 times the cyclic oscillation frequency of a mathematical pendulum with a length of l = 1.25 m. Determine the mass of the spring pendulum, if the spring rate is k = 25N / m. Free fall acceleration modulus g = 10m / s2

To determine the value of the mass of the spring pendulum, we use the ratio: n = ωп / ωм = √ (k / m) / √ (g / l) = √ (k * l / (g * m)), whence we express: m = k * l / (n ^ 2 * g).

Constants and variables: k – spring rate (k = 25 N / m); l is the length of the mathematical pendulum (l = 1.25 m); n is the ratio of the cyclic frequencies of the pendulums (n = 2.5 p); g – acceleration due to gravity (by condition g = 10 m / s2).

Calculation: m = k * l / (n ^ 2 * g) = 25 * 1.25 / (2.5 ^ 2 * 10) = 0.5 kg.

Answer: The mass of the spring pendulum is 0.5 kg.



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