One mathematical pendulum has a period of oscillation of 3s, and the other has a period of 4s.

| September 17, 2021 | education

One mathematical pendulum has a period of oscillation of 3s, and the other has a period of 4s. What is the period of oscillation of a mathematical pendulum, the length of which is equal to the sum of the lengths of the indicated pendulums?

Given: T1 (period of oscillation of the first pendulum) = 3 s; T2 (period of oscillation of the second pendulum) = 4 s.

Constants: g (acceleration due to gravity) = 9.81 m / s2.

1) Length of the first pendulum: T1 = 2Π * √ (l1 / g); l1 / g = T1 ^ 2 / 4Π ^ 2; l1 = T1 ^ 2 * g / 4Π ^ 2 = 3 ^ 2 * 9.81 / (4 * 3.14 ^ 2) ≈ 2.24 m.

2) The length of the second pendulum: l2 = T2 ^ 2 * g / 4Π ^ 2 = 4 ^ 2 * 9.81 / (4 * 3.14 ^ 2) ≈ 3.98 m.

3) The length of the resulting pendulum: l = l1 + l2 = 2.24 + 3.98 = 6.22 m.

4) Period: T = 2Π * √ (l / g) = 2 * 3.14 * √ (6.22 / 9.81) = 5 s.



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