A weight weighing 400 g suspended from a spring vibrates at a frequency of 4 Hz under the action of the spring. Determine the stiffness of the spring.
Data: mgr – weight of the cargo (mgr = 400 g; in the SI system mgr = 0.4 kg); ν is the obtained vibration frequency (ν = 4 Hz).
To find out the required stiffness of the taken spring, we use the formula (we consider a spring pendulum): ν = √ (kx / mgr) / 2Π, whence we express: (kx / mgr) = (ν * 2Π) ^ 2 and kx = mgr * (ν * 2Π) ^ 2.
Let’s perform the calculation: kx = mgr * (ν * 2Π) ^ 2 = 0.4 * (4 * 2 * 3.14) ^ 2 ≈ 252.4 N / m.
Answer: The stiffness of the spring taken should be 252.4 N / m.
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