Question

какой жесткости следует взять пружину,чтобы груз массой 0,1 кг.совершал свободные колебания с периодом 0,3сек

Answer 1

T=2*пи*sqrt(m/k), где m-масса груза, k-жесткость пружины, T-период

k=4*пи^2*m/T^2

k= 4*9.86*0.1/0.09=43.8 (H/м)

Answer 2

Choosing the Spring Stiffness for Free Oscillations

To determine the appropriate spring stiffness for a mass of 0.1 kg to undergo free oscillations with a period of 0.3 seconds, we can use the formula for the period of oscillation of a mass-spring system:

Period of Oscillation (T) = 2π√(m/k)

Where: - T = period of oscillation - m = mass attached to the spring - k = spring stiffness

We can rearrange the formula to solve for the spring stiffness (k):

k = (4π^2 * m) / T^2

Substituting the given values: - m = 0.1 kg - T = 0.3 seconds

We can calculate the spring stiffness (k) using the given values.

k = (4π^2 * 0.1) / (0.3)^2

Calculating the value: - k ≈ 131.59 N/m

Therefore, to achieve free oscillations with a period of 0.3 seconds for a mass of 0.1 kg, a spring stiffness of approximately 131.59 N/m should be chosen.

References

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