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

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.