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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
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.everyall said:When
dv/dt= -qE/m(sin(ωt+φ))
Find v
Then x
By integrating
Yes i like to know how to integrate (sin(ωt+φ))dttopsquark 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
Do you mean ∫sin(t) = -cos(t)malawi_glenn said:Do you know what the primitive function of sin(t) is?
+Ceveryall said:Do you mean ∫sin(t) = -cos(t)
I don't know this because it has 2 variablemalawi_glenn said:+C
Ok. Next. What is the derivative of ##-\cos(\omega t + \varphi )## with respect to ##t##?
Which is plus inside sin function##-\omega t and \varphi##
I still don't know how to integrate sin(a+b)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?
That sucks. Just google it. Chain rule of differentiationeveryall said:I still don't know how to integrate sin(a+b)
I found dy/dx=dy/du*du/dxmalawi_glenn said:That sucks. Just google it. Chain rule of differentiation
yeseveryall said:I found dy/dx=dy/du*du/dx
Does it mean pretend wt+phi =u ?
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.everyall said:Then what is the result after intregrate
The problem says that the electron is initially at rest, so you can determine the value of the constant of integration C.everyall said:From text , i like to know where -eE/mw(cosphi) come ?
Is it should be C instead after integrate sin(wt+phi)
I try to understand physics to discover some new things at 42 year old with high school knowledge.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.
You will discover more if you spend some time doing basic algebra and calculus first. The language of physics is math.everyall said:I try to understand physics to discover some new things at 42 year old with high school knowledge.
Thanks
Diff -cos(wt+phi) = wsin(wt+phi)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.
The velocity and position of an electron in an electromagnetic wave are related through the wave's frequency and wavelength. As the electron moves through the wave, its position changes in a periodic manner determined by the wave's frequency. The velocity of the electron is dependent on the wave's wavelength, with a larger wavelength resulting in a slower velocity and a smaller wavelength resulting in a faster velocity.
The velocity of an electron in an electromagnetic wave is determined by the equation v = λf, where v is the velocity, λ is the wavelength, and f is the frequency. This means that the velocity is directly proportional to the frequency and inversely proportional to the wavelength.
The electric field is the driving force behind the motion of an electron in an electromagnetic wave. As the wave travels through space, the electric field exerts a force on the electron, causing it to move in a periodic manner. The strength of the electric field determines the amplitude of the electron's motion.
The speed of light, denoted by the constant c, plays a crucial role in determining the velocity and position of an electron in an electromagnetic wave. The speed of light is equal to the product of the wave's frequency and wavelength, which means that any changes in frequency or wavelength will result in a change in the speed of light. This, in turn, affects the velocity and position of the electron in the wave.
As an electromagnetic wave is a natural phenomenon, it is not possible to directly control the velocity and position of an electron in the wave. However, by manipulating the properties of the wave such as its frequency and wavelength, it is possible to indirectly affect the velocity and position of the electron. This is the basis for many technologies that utilize electromagnetic waves, such as wireless communication and MRI machines.