Question

СРОЧНО тягар здійснює на пружині А вeртикальні коливання з частотою 1.5Гц. Якою будe частота коливаннь ,якщо підвісити два такі самі тягарі до пружини Б,жорсткість якоіі у 5разів біша від жорсткості пруєини А

Answer 1

V1=√(k/m)/(2*π)
v2=√(5*k/(2*m))=v1*√2.5=1.5*1.58≈2.37 Гц
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Answer 2

Calculation of Frequency for Vertical Oscillations

To calculate the frequency of vertical oscillations when two identical weights are suspended from spring B, which has a stiffness 5 times greater than spring A, we can use the following formula:

Frequency (f) = (1 / 2π) * √(k / m)

Where: - f = frequency of oscillation - k = stiffness of the spring - m = mass of the weight

Given that the frequency of oscillation for a single weight on spring A is 1.5 Hz, we can calculate the frequency for the combined system.

Calculation Steps

1. Calculate the Stiffness of Spring B - Since the stiffness of spring B is 5 times greater than spring A, we can denote the stiffness of spring A as k and the stiffness of spring B as 5k.

2. Calculate the Equivalent Stiffness for the Combined System - When two identical weights are suspended from spring B, the equivalent stiffness k_eq for the combined system can be calculated using the formula: k_eq = 2 * 5k = 10k.

3. Calculate the Frequency for the Combined System - Using the formula mentioned earlier, we can calculate the frequency for the combined system using the equivalent stiffness k_eq.

Final Calculation

Let's calculate the frequency for the combined system using the given values and the steps outlined above.