The period of oscillation of a spring pendulum coincides with the period of oscillation of a mathematical

| May 4, 2021 | education

The period of oscillation of a spring pendulum coincides with the period of oscillation of a mathematical mast with a length of l = 50 cm. Determine the mass of the weight of the spring pendulum if the spring rate is k = 10.

l = 50 cm = 0.5 m.

k = 10 N / m.

g = 10 N / kg.

Tp = Tm.

m -?

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

The periods of the spring Tp and mathematical Tm of the pendulum are determined by the formulas: Tp = 2 * P * √m / √k, Tm = 2 * P * √l / √g.

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

The mass of the weight of the spring pendulum m will be determined by the formula: m = l * k / g.

m = 0.5 m * 10 N / m / 10 N / kg = 0.5 kg.

Answer: the weight of the spring pendulum is m = 0.5 kg.



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