The oscillation period of a mathematical pendulum is n = 2.0 times longer than the oscillation period

| May 8, 2021 | education

The oscillation period of a mathematical pendulum is n = 2.0 times longer than the oscillation period of a spring pendulum with a mass of m = 180 g. Determine the length of the thread of the mathematical pendulum if the stiffness of the spring is k = 15 N / m.

Tm / Tp = 2.

m = 180 g = 0.18 kg.

k = 15 N / m.

g = 10 m / s2.

L -?

The oscillation period T is the time of one complete oscillation.

For a spring pendulum, the period of natural free oscillations Tp is determined by the formula: Tp = 2 * п * √m / √k, where P is the number pi, m is the mass of the load, k is the stiffness of the spring.

For a mathematical pendulum, the period of natural free oscillations Tm is determined by the formula: Tm = 2 * п * √L / √g, where L is the length of the pendulum, g is the acceleration of gravity.

Tm / Tp = 2 * п * √L * √k / √g * 2 * п * √m = √L * √k / √g * √m = 2.

√L = 2 * √g * √m / √k.

L = 4 * g * m / k.

L = 4 * 10 m / s2 * 0.18 kg / 15 N / m = 0.48 m.

Answer: the length of the mathematical pendulum is L = 0.48 m.



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