In 10 seconds the mathematical pendulum makes 10 oscillations. Find the length of the thread?

The oscillation period is a period of time during which the body returns to the same point from which it began its movement.
T = t / n, where n is the number of oscillations, t is the time during which the body made these oscillations.
Let’s define the oscillation period:
T = t / n = 10/10 = 1 s.
The formula for determining the period of oscillation of a mathematical pendulum is:
T = 2π * √ (l / g), where l is the length of the pendulum, g is the free fall acceleration of a body lifted above the Earth by 9.8 m / s².
Let’s square both sides of the formula to get rid of the root:
T² = 4π² * (l / g)
Let us express from this the length of the pendulum l:
l = (T² * g) / (4π²)
Substitute the numerical values ​​and determine the length of the pendulum:
l = (T² * g) / (4π²) = (1² * 9.8) / (4 * 3.14²) = 0.25 m.
Answer: the length of the pendulum is 0.25 m.



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