harmonic oscillations

[tintincute]

hi

i would like to know if you are familiar to this formula. I'm not really sure if this is a harmonic oscillations formula.
does anybody have any idea?
thanks

 

[RadioRon]

hi

i would like to know if you are familiar to this formula. I'm not really sure if this is a harmonic oscillations formula.
does anybody have any idea?
thanks

No, this is a simple formula that describes a function consisting of a constant, or DC component, and an AC component at a single frequency.

 

[dknguyen]

Why is one u a vector and the other not? Seems to be neither should be vectors.

 

[tintincute]

hi Radioron thank you. But this was used in one of our exercises to solve the harmonic oscillation of u(t) mathematically.
do you know where I can get informations about this? Like an examples and explanations.

Thank you again

 

[tintincute]

@dknguyen: they are all "u"

 

[dknguyen]

@dknguyen: they are all "u"

Oh is that just a wrypo (write-po) then?

THe rightmost u has a ^ above it, indicating is a vector of some kind. And then it is being added to u0 which is a magnitude, not a vector...which doesn't make sense.

 

[tintincute]

@dknguyen: hmm, no it's not. it's just a symbol for average value.

 

[dknguyen]

DIfferent notations I guess. Some people use that for peak value or unit vector (Actually I think that's actually peak value. Makes sense since that's the amplitude of the cos wave).

 

[RadioRon]

hi Radioron thank you. But this was used in one of our exercises to solve the harmonic oscillation of u(t) mathematically.
do you know where I can get informations about this? Like an examples and explanations.

Thank you again

I think I have misunderstood you. This formula does indeed describe simple harmonic oscillation.

Harmonic oscillator - Wikipedia, the free encyclopedia

 

[tintincute]

yes you said it right. Different notations.
do you know where I can read some information about this? I would like to fresh up my knowledge.

And another is: I also need information about this:

U^2 = U0^2 + U~^2

i would appreciate it very much.

Thanks

 

[tintincute]

I think I have misunderstood you. This formula does indeed describe simple harmonic oscillation.

Harmonic oscillator - Wikipedia, the free encyclopedia

thank you for this info. But it seems I couldn't find the same formula here.

 

[MrAl]

Hi,

Let me rewrite the equation the way i intend to interpret this:

V(t)=Vdc+Vpk*cos(w*t)

What we have here is a sinusoidal wave with a dc offset Vdc.
In other words, the solution to V(t) includes the sinusoidal part plus the dc offset.

I am not sure what else you may want to know about this however, except maybe
that the frequency F is:
F=w/(2*pi)

so we can rewrite the equation as:

V(t)=Vdc+Vpk*cos(2*pi*F*t)

where
V(t) is the entire solution for the voltage at any point in time t,
Vdc is the dc offset
Vpk is the peak of the sinusoidal part
cos is the trigonometric function cosine
F is the frequency
t is the moment in time we look at the solution, and
pi=the constant 3.14159... and
2 is just another constant.

The period of oscillation is tp=1/F in case you want to know that.