The mathematical pendulum makes 125 oscillations in 300 seconds. what is the length of the thread of this pendulum?
| September 3, 2021 | education
t = 300 s.
n = 125.
g = 10 m / s2.
l -?
The frequency of oscillations of the pendulum v is the number of oscillations that the pendulum makes per unit of time. The oscillation frequency v is determined by the formula: v = n / t, where n is the number of oscillations of the pendulum during time t.
The frequency of free natural oscillations of a mathematical pendulum v is determined by the formula: v = √g / 2 * P * √l, where g is the acceleration of gravity, P is the number pi, l is the length of the thread of the mathematical pendulum.
n / t = √g / 2 * P * √l.
√l = t * √g / 2 * P * n.
l = t ^ 2 * g / 4 * P ^ 2 * n ^ 2.
l = (300 s) ^ 2 * 10 m / s2 / 4 * (3.14) ^ 2 * (125) ^ 2 = 1.46 m.
Answer: the length of the mathematical pendulum is l = 1.46 m.
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