Question

Пружина под действием прикрепленного к ней груза массой 3 кг колеблется с периодом 0,2 с. Определите жесткость пружины.

Answer 1

T=2π√(m/k)

T²=4π²(m/k)

k=4π²m/T²

k=4*3,14*3,14*3/0,2*0,2=2 957,88 (Н/м)

Answer 2

Calculation of the Spring Constant

To determine the spring constant of a spring under the given conditions, we can use the formula for the period of oscillation of a mass-spring system:

T = 2π√(m/k)

where: - T is the period of oscillation, - π is a mathematical constant (approximately 3.14159), - m is the mass attached to the spring, and - k is the spring constant.

In this case, the period of oscillation (T) is given as 0.2 seconds, and the mass (m) is given as 3 kg. We need to solve for the spring constant (k).

Let's rearrange the formula to solve for k:

k = (4π²m) / T²

Substituting the given values:

k = (4π² * 3) / (0.2)²

Calculating the value:

k ≈ 592.48 N/m

Therefore, the spring constant of the given spring is approximately 592.48 N/m.