A body weighing 5 kg performs harmonic oscillations with an amplitude of 10 cm.
| July 24, 2021 | education
A body weighing 5 kg performs harmonic oscillations with an amplitude of 10 cm. The maximum kinetic energy of an oscillating body is 2.5 J. Determine the period of oscillation.
Given: m (mass of the oscillating body) = 5 kg; A (amplitude of harmonic vibrations) = 10 cm = 0.1 m; Ekmax (maximum kinetic energy) = 2.5 J.
To determine the period of harmonic oscillations, we use the formula: E (total energy) = Ekmax = m * A ^ 2 * ω ^ 2/2 = m * A ^ 2 * (2 * Π / T) ^ 2/2 = 2 * m * A ^ 2 * Π ^ 2 / T ^ 2, whence we express: T = √ (2 * m * A ^ 2 * Π ^ 2 / Ekmax).
Calculation: T = √ (2 * 5 * 0.1 ^ 2 * 3.14 ^ 2 / 2.5) = 0.628 s.
Answer: The period of harmonic oscillations of a given body is 0.628 s.
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