How do I integrate this?

  • #1
Ivegottheskill
11
0
An L-C circuit will undergo resonance, with the current varying sinusoidally, where:
I(t) = I*cos(omega*t)

I keep getting stuck with an answer of I*t*sin(omega*t)

Can't find anything on the standard table of integrals that would indicate this is incorrect

:confused:
 

Answers and Replies

  • #2
Fermat
Homework Helper
872
1
How did you get the answer of I*t*sin(omega*t)
 
  • #3
schattenjaeger
178
0
I*cos(omega*t)

omega's just a constant then? I'll call it a

I*cos(at)

I's a constant too, so you'll only integrat cos(at)

which should be sin(at)/a

so I*sin(omega*t)/omega?

Other possibility, since I'm not sure myself, is that you can express omega as a function of time, can't you? (2pi*frequency)and frequency is like 1/t or something. I dunno, I think the first way's right

Edit: Wait, I isn't a constant, well whatever, I'll leave this post up here for learning purposes but methinks it's rubbish
 
  • #4
Fermat
Homework Helper
872
1
so I*sin(omega*t)/omega?
That looks correct. I wasn't sure what you were integrating.

omega isn't a funtion of time - it is a constant.

omega is only a funtion of time if it varies with time.
frequency isn't a function of time either, but usually, a constant value. frequency is simply the rate at which something changes wrt time. But that rate of change is constant!
 
  • #5
Nylex
552
2
schattenjaeger said:
Edit: Wait, I isn't a constant, well whatever, I'll leave this post up here for learning purposes but methinks it's rubbish

That I is a constant - it's the value of the current at time t = 0 (usually).
 
  • #6
Ivegottheskill
11
0
Thanks I'll give that a shot. Sorry for the confusion, omega was a constant (angular frequency). I'm worried about how much high school stuff I've already forgotten :eek:

I wasn't sure how to properly intergrate in that case.

I tried looking it up, but could only find the simple cases (i.e. integrate sin x = cos x)
 
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