Question

При какой скорости поезда пружинный маятник массой 200 г, и жесткостью пружины 20 Н/м находящийся в вагоне, особенно сильно раскачается, если расстояние между стыками рельсов 20 м?

Answer 1

m=0.2 кг   k=20 Н/м    L=20 м    v=?

T=2*π*√(m/k)  - период колебаний маятника

v=L/T=L/(2*π*√(m/k))=20/(2*3.14*√(0.2/20))≈32 м/с   (115 км/ч)

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Answer 2

Calculation of the Speed of the Train

To calculate the speed at which the spring pendulum, with a mass of 200 g and a spring stiffness of 20 N/m, located in a train car, will swing particularly strongly, we can use the formula for the natural frequency of a spring-mass system:

Natural frequency (f) = (1 / (2π)) * √(k / m)

Where: - f = natural frequency - k = spring stiffness - m = mass of the pendulum

Substituting the given values: - k = 20 N/m - m = 200 g = 0.2 kg

We can calculate the natural frequency using the given formula.

Calculation

The natural frequency (f) can be calculated as follows: f = (1 / (2π)) * √(k / m)

Substituting the given values: f = (1 / (2π)) * √(20 / 0.2) f ≈ 5.02 Hz

Conclusion

Therefore, the spring pendulum, with a mass of 200 g and a spring stiffness of 20 N/m, located in a train car, will swing particularly strongly at a natural frequency of approximately 5.02 Hz.