Harmonic motion of a light bulb using a mathematical pendulum as an example
</figcaption>
</figure>
</center>
<p>
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: <a href="https://doi.org/10.1016/S0042-6989(99)00084-X">doi.org/10.1016/S0042-6989(99)00084-X</a>), then the longer the body is at a certain point, the brighter it seems to the retina of our eye</p><p>
The perceived energy is inversely proportional to the time spent in a given place:
$$ W\sim\Delta t $$
@@ -73,7 +73,7 @@
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
−
$$ v(t) = \dot{x}(t) =\omega\cdot x_0\cos\omega t $$
+
$$ v(t) = \dot{x}(t) =\omega\cdot x_0\cos\omega t $$
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.
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
Harmonic motion of a light bulb using a mathematical pendulum as an example
Harmonic motion of a light bulb using a mathematical pendulum as an example
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
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: <a href="https://doi.org/10.1016/S0042-6989(99)00084-X">doi.org/10.1016/S0042-6989(99)00084-X</a>), then the longer the body is at a certain point, the brighter it seems to the retina of our eye</p><p>
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: <a href="https://doi.org/10.1016/S0042-6989(99)00084-X">doi.org/10.1016/S0042-6989(99)00084-X</a>), then the longer the body is at a certain point, the brighter it seems to the retina of our eye</p><p>
The perceived energy is inversely proportional to the time spent in a given place:
The perceived energy is inversely proportional to the time spent in a given place:
$$ W\sim\Delta t $$
$$ W\sim\Delta t $$
@@ -73,7 +73,7 @@
In harmonic motion, the position of the light bulb is described by the expression
In harmonic motion, the position of the light bulb is described by the expression
$$ x(t) = x_0 \sin\omega t $$
$$ x(t) = x_0 \sin\omega t $$
From here, the speed value changes as
From here, the speed value changes as
$$ v(t) = \dot{x}(t) =\omega\cdot x_0\cos\omega t $$
$$ v(t) = \dot{x}(t) =\omega\cdot x_0\cos\omega t $$
The lower the speed, the more time it takes for the light bulb to cover equal intervals of time.
The lower the speed, the more time it takes for the light bulb to cover equal intervals of time.
$$ v\sim\frac{1}{\Delta t}$$
$$ v\sim\frac{1}{\Delta t}$$
Thus, when the speed of the light bulb during harmonic motion is minimal, the energy perceived by the eye becomes greater.
Thus, when the speed of the light bulb during harmonic motion is minimal, the energy perceived by the eye becomes greater.
$$ W\sim\frac{1}{v}$$
$$ W\sim\frac{1}{v}$$
Thus, the bulb appears brighter in places where its speed is minimal, i.e. at its extreme points.
Thus, the bulb appears brighter in places where its speed is minimal, i.e. at its extreme points.
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
