# Calculate the oscillation period of a mathematical pendulum 2.5 m long. Calculate vibration frequency, cyclic frequency.

May 29, 2021 | education

| 1. Formula for determining the oscillation frequency of a mathematical pendulum:

ν = (1 / 2π) * √ (g / l), where g is the acceleration of gravity, l is the length of the mathematical pendulum.

Let’s plug in the numbers and find the frequency:

ν = (1 / 2π) * √ (9.8 / 2.5) = 0.99 Hz.

2. The oscillation period depends on the frequency according to the law:

T = 1 / ν

Substitute the numbers and find the period:

T = 1 / ν = 1 / 0.99 = 1.01 s.

3. Cyclic frequency is the number of vibrations made by the body in 2π seconds:

ω = 2π / T

Substitute the numbers and find the cyclic frequency:

ω = 2π / T = 2π / 1.01 = 6.22 rad / s.

Answer: the oscillation period is 1.01 s, the frequency is 0.99 s, and the cyclic frequency is 6.22 rad / s.

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.