The spring pendulum oscillates with a period of 2 seconds, the weight of the load is 200 g. Determine the stiffness of the spring.

In the condition, the period of oscillation of the load on the spring is specified: T = 2 s.

The oscillation period of the spring pendulum is determined by the formula:

T = 2π (M / k) ^ 1/2,

where M is the mass of the cargo, M = 200 g = 0.2 kg; k is the stiffness of the spring, N / m.

Squaring the left and right sides of the formula for the period T, we get:

T 2 = 4π ^ 2 M / k,

whence the required spring stiffness:

k = 4 π ^ 2 M / T 2 = 4 × 3.14 ^ 2 × 0.2 / 2 ^ 2 = 1.97 N / m.

Answer: 1.97 N / m.




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