Why does a rapidly oscillating bulb on a spring seem to flash at the extreme points of its trajectory?

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    <h3> Statement </h3>
    <p>
        $3.1.4.$ Why does a rapidly oscillating bulb on a spring seem to flash at the extreme points of its trajectory?
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    <h3>Solution</h3>
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The power of the light bulb, and as a consequence the intensity of the light bulb, remains constant, so the longer the light bulb is at a certain moment, the more energy comes to the eye. Because the human eye perceives and accumulates light energy at a particularly high frequency of change (more details: doi.org/10.1016/S0042-6989(99)00084-X), then the longer the body is at a certain point, the brighter it seems to the retina of our eye

The perceived energy is inversely proportional to the time spent in a given place:
$$W\sim\Delta t$$
In harmonic motion, the position of the light bulb is described by the expression
$$x(t) = x_0 \sin\omega t$$
From here, the speed value changes as
$$v(t) = \dot{x}(t) =\omega \cdot x_0\cos \omega t$$
The lower the speed, the more time it takes for the light bulb to cover equal intervals of time.
$$v\sim\frac{1}{\Delta t}$$
Thus, when the speed of the light bulb during harmonic motion is minimal, the energy perceived by the eye becomes greater.
$$W\sim \frac{1}{v}$$
Thus, the bulb appears brighter in places where its speed is minimal, i.e. at its extreme points.

	<p style="text-align: right; font-style: italic; font-size: 14;">
      Aliaksandr Melnichenka<br>
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