A body of mass m, suspended from the end of the spring, vibrates at a frequency of 0.6 Hz. Determine the mass

| February 11, 2021 | education

A body of mass m, suspended from the end of the spring, vibrates at a frequency of 0.6 Hz. Determine the mass of this body if it is known that after hanging another body with a mass of m1 = 500 g, the resulting system oscillates with a period of T1 = 2.5 s.

Data: ν1 (vibration frequency of the first body) = 0.6 Hz; m2 (mass of the second suspended body) = 500 g = 0.5 kg; T1.2 (period of oscillation of the system of two bodies) = 2.5 s.

1) The vibration frequency of the first body: ν1 = 1 / 2Π * √ (k / m1), whence 2Π = √ (k / m1) / ν1.

2) The oscillation period of the system: T1.2 = 2Π * √ ((m1 + m2) / k), whence 2Π = T1.2 / √ ((m1 + m2) / k).

3) Let’s compose and solve the equation: Т1.2 / √ ((m1 + m2) / k) = √ (k / m1) / ν1.

2.5 / √ ((m1 + 0.5) / k) = √ (k / m1) / 0.6.

6.25 / ((m1 + 0.5) / k) = (k / m1) / 0.36 | * 0.36.

2.25k / (m1 + 0.5) = k / m1 | : k.

2.25m1 = m1 + 0.5.

1.25m1 = 0.5 and m1 = 0.5 / 1.25 = 0.4 kg.

Answer: A body weighing 0.4 kg was suspended from the spring.



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