act 3 reconoc u1 fisica mod.docx

7/30/2019 Act 3 Reconoc U1 FISICA MOD.docx

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Act 3 : Reconocimiento Unidad I

Leccin de Reconocimiento de la Unidad I

Estimado estudiante, se espera que a travs de esta leccin se realice el reconocimiento a la unidad 1:Vibraciones y Ondas. Abordar una serie de lecturas que debe realizar comprensivamente. Esto es, seharn algunas preguntas referentes a cada una y debe elegir la respuesta acertada. Si en primerainstancia no le es posible alcanzar el resultado esperado, lo puede volver a intentar.xitos en este trabajo de lectura.

Movimiento Peridico y Movimiento armnico Simple

Un movimiento es peridico cuando la funcin que representa la posicin se repite en intervalos iguales de tiempo, el

intervalo mnimo de este tiempo se llama periodo. Es decir, si tenemos la coordenada , el movimiento es

peridico si , donde se llama el periodo.

Se denomina movimiento armnico simple, a aquel movimiento que esta dado de la siguiente forma:

Donde t es el tiempo y A, y son constantes, las cuales se llaman: A amplitud, frecuencia angular y fase inicial;a todo el argumento que est dentro de la funcin coseno se le llamara fase.

La anterior expresin tambin se puede escribir de las siguientes formas:

Donde: , y estn relacionadas con y .


Cul de las siguientes afirmaciones es verdadera:

1. Todo movimiento periodico tiene que ser un movimiento armnico simple.

2. Todo movimiento armnico simple es un movimiento periodico.

6506 continue 17145 Bu1km2QC1N

Ninguna de esas opciones.

Las dos opciones: 1 y 2

La opcin 2

La opcin 1

Movimiento Armnico como la proyeccin de un Movimiento circular

El movimiento armnico simple se puede considerar como la proyeccin sobre un eje de un movimientocircular uniforme, esto quiere decir lo siguiente:

Se considera una partcula que gira con una velocidad angular constante siguiendo una circunferencia de
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radio , que parte desde un ngulo inicial , por lo cual el ngulo esta cambiando de la forma

, si queremos hallar las coordenadas x y y de la posicin de esta partcula, entoncesmultiplicamos el radio de la circunferencia por el coseno y el seno del ngulo calculado anteriormente, lo cual

es: y .Comparando esto con el M.A.S., encontramos que precisamente la coordenada x de la posicin de la partculaes un M.A.S.:


Un cuerpo de masa , tiene un movimiento circular de radio , y gira dando

una vuelta cada . Si el ngulo inicial desde donde parti es de , entonces la coordenada x, de estemovimiento es:



Un cuerpo de masa , tiene un movimiento circular de radio , y gira dando

una vuelta cada . Si el ngulo inicial desde donde parti es de , entonces la coordenada x, de estemovimiento es:

Su respuesta :

Correcto

Vectores rotatorios complejos

Otra forma en que se puede representar un M.A.S. es con ayuda de vectores rotatorios complejos, para estoconsideremos la coordenada x de un vector rotatorio, con lo cual nos da pie para poder imaginarnos un plano,donde un eje sea real (por ejemplo x) y el otro sea imaginario. Este es el caso de un plano complejo. Un
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3/6

nmero complejo se puede representar con vectores en este plano, ya que la suma de nmeros complejoscumple tambin con la regla del paralelogramo de los vectores, sin embargo se ha de?nido el producto entre

nmeros complejos, lo cual hace la diferencia con los vectores en .

El nmero complejo se puede escribir de varias formas: o

o donde:A se llama el modulo de y es elargumento de . Esta ltima notacin se llama la notacin de Euler, la cual es la que se va a utilizar; ya quecon esta notacin se entiende mejor la operacin de la multiplicacin entre nmeros complejos, o sea, si semultiplican dos nmeros complejos, se multiplican los mdulos y se suman los argumentos: Si

y entonces:

; donde: y

. Al multiplicar cualquier nmero por un exponente complejo, el resultado es simplemente larotacin de este nmero un ngulo igual al argumento del exponente.

Por todo lo anterior entonces nos podemos imaginar un movimiento amnico simple como la parte real de unvector rotatorio complejo:

.


El nmero complejo , tiene un mdulo que es igual a:


5

3,5

4

7


El argumento o fase, del siguiente nmero complejo es:

http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{3}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{4}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{6}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{2}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z=1+ihttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z=3+i4http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?x+=+Real/{Ae^{i(/omega+t+/alpha)}/}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/theta+=+/theta_1++/theta_2http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?A+=+A_1/cdot+A_2http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z=Z_1/cdot+Z_2+=+A_1/cdot+A_2e^{i/theta_1}/cdot+e^{i/theta_2}+=+Ae^{i/theta}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z_2+=+A_2e^{i/theta_2}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z_1+=+A_1e^{i/theta_1}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Zhttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/thetahttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Zhttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z+=A+e^{i/theta}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z=A(cos(/theta+)+isen(+/theta))http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z+=+x++iyhttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?R^2http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{3}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{4}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{6}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{2}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z=1+ihttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z=3+i4http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?x+=+Real/{Ae^{i(/omega+t+/alpha)}/}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/theta+=+/theta_1++/theta_2http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?A+=+A_1/cdot+A_2http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z=Z_1/cdot+Z_2+=+A_1/cdot+A_2e^{i/theta_1}/cdot+e^{i/theta_2}+=+Ae^{i/theta}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z_2+=+A_2e^{i/theta_2}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z_1+=+A_1e^{i/theta_1}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Zhttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/thetahttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Zhttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z+=A+e^{i/theta}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z=A(cos(/theta+)+isen(+/theta))http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z+=+x++iyhttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?R^2http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{3}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{4}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{6}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{2}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z=1+ihttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z=3+i4http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?x+=+Real/{Ae^{i(/omega+t+/alpha)}/}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/theta+=+/theta_1++/theta_2http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?A+=+A_1/cdot+A_2http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z=Z_1/cdot+Z_2+=+A_1/cdot+A_2e^{i/theta_1}/cdot+e^{i/theta_2}+=+Ae^{i/theta}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z_2+=+A_2e^{i/theta_2}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z_1+=+A_1e^{i/theta_1}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Zhttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/thetahttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Zhttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?Z+=A+e^{i/theta}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z=A(cos(/theta+)+isen(+/theta))http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?z+=+x++iyhttp://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?R^2http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{3}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{4}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{6}http://campus07.unadvirtual.org/moodle/filter/tex/displaytex.php?/frac{/pi}{2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4/6


El argumento o fase, del siguiente nmero complejo

es:

Su respuesta :

Correcto


El producto de los siguientes nmeros complejos y

es:

Su respuesta :

10

Correcto


El modulo de la suma de los siguientes nmeros y es:


5

7

8

9

El argumento o fase del producto de los siguientes nmeros y es:

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