A load weighing 400 g vibrates with an amplitude of 15 cm on a spring with a stiffness of 25 N / m. Write the equation for the vibrations of the load.
1) Harmonic oscillations, i.e. such oscillations that are expressed by a sinusoidal function, arise when the restoring force is proportional to the displacement from the equilibrium position, but has the opposite sign:
F = – k * x.
2) For such a dependence, the offset x is expressed by the function:
x = x0 * sin (ωt), where
x0 – vibration amplitude,
ω is the angular frequency of the oscillation.
3) The angular frequency depends on the stiffness of the spring and the mass of the load as follows:
ω = √ (k / m) = √ (25 / 0.4) ≈ 7.9 (1 / s).
Therefore, we get the following equation for this oscillation:
x = 0.15 * sin (7.9t).
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