Determine the period and frequency of oscillations of a mathematical pendulum 40 cm long.

| March 4, 2021 | education

Determine the period and frequency of oscillations of a mathematical pendulum 40 cm long. How many oscillations will such a pendulum make in 0.5 minutes?

To determine the period and frequency of oscillations of a mathematical pendulum with a length of L = 40 cm = 0.4 m, we use the formula for the period of a mathematical pendulum T = 2 ∙ π ∙ (L / g) ^ (1/2), where g = 9.8 m / (c ^ 2) – free fall acceleration. T = 2 ∙ π ∙ (0.4 / 9.8) ^ (1/2) ≈ 2 ∙ π ∙ 0.2 ≈ 1.269 (s), then the frequencies n = 1 / T; n = 1 / 1.269 ≈ 0.788 (c ^ (- 1)). To determine how many oscillations such a pendulum will make in t = 0.5 min = 30 s, we will use the definition of the oscillation period of a mathematical pendulum T = t / N, where N is the number of oscillations made by this pendulum during a given time. We express N = t / T, we get N = t / T; N = 30 / 1.269 = 23.64 (fluctuations).
Answer: 1.269 s; 0.788 s ^ (- 1); 23.64 vibrations.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.