The oscillation period of a mathematical pendulum is 2 times greater than the oscillation period of a spring

| July 18, 2021 | education

The oscillation period of a mathematical pendulum is 2 times greater than the oscillation period of a spring pendulum with a mass of 180 g, determine the length of the thread of the mathematical pendulum, if the rigidity is 15, the modulus of gravitational acceleration is 10.

m = 180 g = 0.18 kg.

Tm / Tp = 2.

g = 10 N / kg.

k = 15 N / m.

l -?

The period of oscillation T is the time of one complete oscillatory movement of the pendulum.

The period of the mathematical Tm and the spring Tp of the pendulum is determined by the formulas: Tm = 2 * P *

√l / √g, Тп = 2 * П * √m / √k.

Since according to the condition of the problem: Tm / Tp = 2, then 2 * P * √l * √k / 2 * P * √m * √g = 2.

√l = 2 * √m * √g / √k.

l = 4 * m * g / k.

l = 4 * 0.18 kg * 10 N / kg / 15 N / kg = 0.48 m.

Answer: the mathematical pendulum has a length of l = 0.48 m.



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