Given a mathematical pendulum with a length of 3.5 m and a weight of 7 kg, which is equal to the stiffness of the spring

Given a mathematical pendulum with a length of 3.5 m and a weight of 7 kg, which is equal to the stiffness of the spring, if, when this weight is suspended from the spring, the oscillation period is equal to the oscillation period of the above mathematical pendulum.

Given a mathematical pendulum with a length of L = 3.5 m and a load of mass m = 7 kg. The period of its oscillations is found by the formula: Т₁ = 2 · π · √ (L / g), where g ≈ 9.8 N / kg, π ≈ 3.14. When this weight is suspended from the spring, the oscillation period of the spring pendulum T₂ turned out to be equal to the oscillation period of the above mathematical pendulum Т₁ = Т₂, where Т₂ = 2 · π · √ (m / k), k is the spring stiffness. To determine what the stiffness of the spring is equal to, we equate these expressions: 2 π √ (L / g) = 2 π √ (m / k), then:

k = m g / L.

We get:

k = (7 kg 9.8 N / kg) / 3.5 m;

k = 19.6 N / m.

Answer: the spring rate is 19.6 N / m.