A weight of 0.10 kg hanging on a spring makes vertical vibrations with an amplitude of 4.0 cm.

| May 6, 2021 | education

A weight of 0.10 kg hanging on a spring makes vertical vibrations with an amplitude of 4.0 cm. Determine: the period of harmonic vibrations of the load, if a force of 0.10 N is required for the elastic elongation of the spring by 1.0 cm; energy of harmonic oscillations of the pendulum. Disregard the mass of the spring.

To find the values ​​of the period of harmonic vibrations of the specified load and the vibration energy, we will use the formulas: T = 2 * * * √ (m / k) = 2 * Π * √ (m * Δx / F) and E = k * A ^ 2/2 = F * A ^ 2 / (2 * Δx).

Variables: m is the mass of the cargo (m = 0.1 kg); Δx – elastic elongation of the spring (Δx = 1 cm = 0.01 m); F – tensile force (F = 0.1 N); A is the amplitude of fluctuations of the load (A = 4 cm = 0.04 m).

Calculation: a) Period: T = 2 * Π * √ (m * Δx / F) = 2 * 3.14 * √ (0.1 * 0.01 / 0.1) = 0.628 s;

b) Energy of harmonic vibrations: E = F * A ^ 2 / (2 * Δx) = 0.1 * 0.04 ^ 2 / (2 * 0.01) = 0.008 J = 8 mJ.

Answer: The oscillation period is 0.628 s; the energy of harmonic vibrations is 8 mJ.



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