Find v and x of electron in an electromagnetic wave

everyall
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Thread moved from the technical Math forums, and OP is reminded to show their work on their schoolwork questions
When
dv/dt= -qE/m(sin(ωt+φ))

Find v
Then x
By integrating
 
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everyall said:
When
dv/dt= -qE/m(sin(ωt+φ))

Find v
Then x
By integrating
Well, if you have dv/dt, then integrate it to get v as a function of t. Then v = dx/dt. Integrate that to get x as a function of t.

Is your question how to integrate this?

-Dan
 
topsquark said:
Well, if you have dv/dt, then integrate it to get v as a function of t. Then v = dx/dt. Integrate that to get x as a function of t.

Is your question how to integrate this?

-Dan
Yes i like to know how to integrate (sin(ωt+φ))dt
 
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Do you know what the primitive function of sin(t) is?
 
malawi_glenn said:
Do you know what the primitive function of sin(t) is?
Do you mean ∫sin(t) = -cos(t)
 
everyall said:
Do you mean ∫sin(t) = -cos(t)
+C

Ok. Next. What is the derivative of ##-\cos(\omega t + \varphi )## with respect to ##t##?
 
malawi_glenn said:
+C

Ok. Next. What is the derivative of ##-\cos(\omega t + \varphi )## with respect to ##t##?
I don't know this because it has 2 variable
##-\omega t and \varphi##
Which is plus inside sin function

How to solve this
 
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Likes malawi_glenn
No ##\omega## is constant pretend that is has value say 2.78 or whatever
Did you not learn about the chain rule in school?
 
malawi_glenn said:
No ##\omega## is constant pretend that is has value say 2.78 or whatever
Did you not learn about the chain rule in school?
I still don't know how to integrate sin(a+b)
 
  • #10
everyall said:
I still don't know how to integrate sin(a+b)
That sucks. Just google it. Chain rule of differentiation
 
  • #11
malawi_glenn said:
That sucks. Just google it. Chain rule of differentiation
I found dy/dx=dy/du*du/dx
Does it mean pretend wt+phi =u ?
Then what is the result after intregrate
 
  • #12
Screenshot_2023-05-25-21-51-52-186_com.google.android.apps.docs-edit.jpg

From text , i like to know where -eE/mw(cosphi) come ?

Is it should be C instead after integrate sin(wt+phi)
 
  • #13
everyall said:
I found dy/dx=dy/du*du/dx
Does it mean pretend wt+phi =u ?
yes
everyall said:
Then what is the result after intregrate
Well figure out what the derivative of ##-\cos(\omega t + \varphi)## is then it should be pretty easy to figure out what the primitive function to ## \sin(\omega t + \varphi)## is.

Out of curiousity, why are you doing this problem if you have not taken approriate math classes?

everyall said:
From text , i like to know where -eE/mw(cosphi) come ?

Is it should be C instead after integrate sin(wt+phi)
The problem says that the electron is initially at rest, so you can determine the value of the constant of integration C.
 
  • #14
malawi_glenn said:
yes

Well figure out what the derivative of ##-\cos(\omega t + \varphi)## is then it should be pretty easy to figure out what the primitive function to ## \sin(\omega t + \varphi)## is.

Out of curiousity, why are you doing this problem if you have not taken approriate math classes?The problem says that the electron is initially at rest, so you can determine the value of the constant of integration C.
I try to understand physics to discover some new things at 42 year old with high school knowledge.
Thanks
 
  • #15
everyall said:
I try to understand physics to discover some new things at 42 year old with high school knowledge.
Thanks
You will discover more if you spend some time doing basic algebra and calculus first. The language of physics is math.
 
  • #16
malawi_glenn said:
yes

Well figure out what the derivative of ##-\cos(\omega t + \varphi)## is then it should be pretty easy to figure out what the primitive function to ## \sin(\omega t + \varphi)## is.
Diff -cos(wt+phi) = wsin(wt+phi)

Screenshot_2023-05-25-22-46-09-734_com.google.android.apps.docs-edit.jpg

Where this term come from
 
  • #17
I wrote it earlier in this thread.

## \dfrac{\text d v}{\text d t} = - \dfrac{eE_0}{m}\sin (\omega t - \varphi)##

You now know that the derivative of ##-\cos (\omega t - \varphi) ## is ## \omega \sin (\omega t - \varphi)##

Then you also know this, that the derivative of ##-\dfrac{1}{\omega}\cos (\omega t - \varphi) ## is ## \sin (\omega t - \varphi)##

It should not too hard to figure out what ##v(t)## is now.
 
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