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| <h3 id="back-link"><a href="../../#3.1">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#3.1">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
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| $3.1.4.$ Why does a rapidly oscillating bulb on a spring seem to flash at the extreme points of its trajectory? | | $3.1.4.$ 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> | | <h3>Solution</h3> |
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| 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 |
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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: <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: |
| $$ W\sim\Delta t $$ | | $$ W\sim\Delta t $$ |
| 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. |
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| <p style="text-align: right; font-style: italic; font-size: 14;"> | | <p style="text-align: right; font-style: italic; font-size: 14;"> |
| Aliaksandr Melnichenka<br> | | Aliaksandr Melnichenka<br> |
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