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# Circuit theory Watch

1. Hi folks its the annoying me again, I've got another problem i need some advice on, although i don't expect anyone to complete my problems i always appreciate the advice and the guidance i recieve off you intelligent folks. For this particular question I just need advice on how to start the question and which part of the tutorials notes I should look at.

A complex waveform is given by the expression

V = 100 sin(100πt) + 50 sin(200πt + π/8)

Determine:-
a) The amplitude of the fundamental
2. Which bit are you having the trouble with?
A*sin(omega*t + phi)
is just a way of describing a sine wave with amplitude = A, frequency = omega/2pi, and phase angle = phi.
3. So you have a voltage which is represented by the sum two waveforms: the first max amplitude is double that of the second but also it's only half the frequency of the second, which is also phase shifted by pi/8 rad in relation to the first.
4. (Original post by Joinedup)
Which bit are you having the trouble with?
A*sin(omega*t + phi)
is just a way of describing a sine wave with amplitude = A, frequency = omega/2pi, and phase angle = phi.
Im having difficulty calculating it I don't know where to start
5. (Original post by sunny1982)
Im having difficulty calculating it I don't know where to start
well you've got two sine waves being added together.
If we call them s1 and s2 we have
s1 = 100sin(100*pi*t)
s2 = 50sin(200*pi*t + pi/8)

so you can already write a table for each of s1 and s2 showing it's amplitude, frequency and phase angle.
6. so what is t in the equations?
7. (Original post by sunny1982)
so what is t in the equations?
time
8. (Original post by Joinedup)
time
How do i go about finding t?
9. (Original post by sunny1982)
How do i go about finding t?
you don't need to find t for that question. t is the variable controlling the output of the function, you can put in any value for t and it'll tell you what the voltage is at that instant.
10. So ive calculate s1 and s2

S1 = 309.386
S2 = 481.621

Do I add these together to get the fundamental amplitude? bare in mind I have not calculated t in the equation.
11. (Original post by sunny1982)
So ive calculate s1 and s2

S1 = 309.386
S2 = 481.621

Do I add these together to get the fundamental amplitude? bare in mind I have not calculated t in the equation.
sin (x) must be greater or equal to -1 and less or equal +1 for any value of x.
100 * sin(anything) can't be more than 100 (or less than -100)
50sin(anything) can't be more than 50 or less than -50.

I think you need to revise your trigonometry, circular motion and simple harmonic motion before attempting AC questions.
12. The amplitude of the fundamental frequencies are given by the A multiplier in the A*Sin(omega*t + phi) parts. Phi is either pi/8 or 0 rad.

To analyse the waveform mathematically to find the maximum amplitude of the complex waveform at some time t seconds you will need:

Trig identities for the double angle formula: Sin(A+B)

Differentiate the expanded trig identity using the product rule and solve for t to find where the rate of change is 0. i.e. at max and min amplitudes,
dv/dt = 0.

Analyse the points of max, min and inflexion because the composite waveform has 4 solutions where dv/dt = 0 and all are at different amplitudes.

Substitute the four values of t into the original equation to find the solution for the maximum composite amplitudes.
13. Thanks for your help folks but I think I'm going to need some private tuition on this subject, I'm going to look for a tutor or do you folks know of any?
14. This question is imo too hard for 6th form, which is how you flagged it. Are you trying to read ahead of the syllabus?
I think the maximum you need for a level is knowing how you *can* describe a sine wave with V=Asin(omega*t + phi) rather than doing anything clever with it (like this question)... and that was back in the 1980's when there was more ac in the syllabus.

You should be able to work out V at a given t from those eqn. though. Just work out the contents of the brackets first, put your calculator into radians and take the sine. Then multiply by the amplitude.
15. (Original post by Joinedup)
You should be able to work out V at a given t from those eqn. though. Just work out the contents of the brackets first, put your calculator into radians and take the sine. Then multiply by the amplitude.
Waveform analysis A sin omega t + phi.pdf

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