# stuck on rearranging this question, frequency and periodic time

#### ninjaman

Joined May 18, 2013
341
hello,

I am reading a book on principles and applications, the is a list of questions for you to answer. so far i have been doing ok with. but one has me a little stuck on getting to the correct answer. some how i managed to find some of the answer and some of my thinking was right. but i cant get the exact answer. i have looked at the answer at the end of the chapter and worked my way around it but was hoping for there to be a way that i could understand. i have tried rearranging the formula to get the right answre.

here is the question
dteremine the frequency and periodic time for an alternating emf having an instantaneous voltage of 5v, 0.02 seconds after passing through zero if the peak value is 12v.
there are examples in the book that i looked at that gave me some idea. i wrote out the formula like this
5v = 12v sin(2pi * ? * 0.02), i tried to rearrange this and got 3.324 which is close to the answer. divide everything by 5 except what i dont have, the frequency.
then i looked at an example
5/12 = 0.416, this inverse sin 0.416 = 0.42977 (rad) which is getting somewhere closer i think. convert this to degrees to get 24.62, put this in 12vsin(24.62) = 4.99volts. so 0.42977 has something to do with the answer. after mucking around i got 0.42977/ 2pi * 0.02 = 3.42 Hz which is close and 1 / 3.42 = 0.29

I dont know if there is a better way than to look at the answer and muck about with it. i dont feel like i have understood the question or how to do it.....because i havent and i cant.

thanks
simon

#### wayneh

Joined Sep 9, 2010
17,498
Well first I'd start with the assumptions. First you assumed the wave shape of the alternating emf was a sine wave. That's a reasonable and simplifying assumption.

Then you assumed that 0.02 seconds after a zero crossing was still in the first quarter of the cycle, the positive-going peak. With no other information given I'd be reluctant to make that assumption. But without it, the answer is a family of waves instead of one unique wave. If you decide to go after the lowest frequency solution, that's reasonable. It's the kind of question that could trip you up on an exam, though.

OK, on to the numbers. I believe you've made the calculations correctly but you may be getting hung up on rounding imprecisions. Do the calculations in a spreadsheet or on your calculator without rounding. I get 3.420Hz from your first equation. Remember to use 2π when you're using radians and 360 when you're using degrees.

#### shteii01

Joined Feb 19, 2010
4,644
v=A*sin(2*pi*f*t)
A=12 volts
t=0.02 seconds
v=5 volts

5=12*sin(2*3.14*f*0.02)
5/12=sin(2*3.14*f*0.02)
0.4166=sin(0.1256*f)
inverse sin(0.4166)=0.4297
0.4297=0.1256*f
f=3.421 Hz

Did you see degrees anywhere?

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#### shteii01

Joined Feb 19, 2010
4,644
Well first I'd start with the assumptions. First you assumed the wave shape of the alternating emf was a sine wave. That's a reasonable and simplifying assumption.

Then you assumed that 0.02 seconds after a zero crossing was still in the first quarter of the cycle, the positive-going peak. With no other information given I'd be reluctant to make that assumption. But without it, the answer is a family of waves instead of one unique wave. If you decide to go after the lowest frequency solution, that's reasonable. It's the kind of question that could trip you up on an exam, though.

OK, on to the numbers. I believe you've made the calculations correctly but you may be getting hung up on rounding imprecisions. Do the calculations in a spreadsheet or on your calculator without rounding. I get 3.420Hz from your first equation. Remember to use 2π when you're using radians and 360 when you're using degrees.
I think his second assumption is based on the fact that at t=0.02 seconds the voltage is 5 volts, and it will eventually peak at 12 volts some time later. So you can see how the sine is rising from 0 to 5 on the way to the 12.

#### wayneh

Joined Sep 9, 2010
17,498
It could be on its 5th or 500th trip from 0 to 12V at the 20ms mark. There's no way to know except to guess.

#### wayneh

Joined Sep 9, 2010
17,498
f=3.421 Hz
Sorry to niggle, but you shouldn't report an answer to 3 digits when you have rounded pi to just two in your calculations.

#### DGElder

Joined Apr 3, 2016
351
"I dont know if there is a better way than to look at the answer and muck about with it. i dont feel like i have understood the question or how to do it.....because i havent and i cant."

Yes, there is a better way: first learn algebra and trigonometry, then electronics. You can't pursue a serious course in electronics by mucking about with trial and error to match given solutions in a text. The skills you need are at least a basic understanding of the applicable physics and basic high school math. These are useful even for an electronics hobby, but for pursuit of a career they are essential. Even if you find a job with very little math involved you still need it to work through an electronics education and math is a fundamental tool for learning how electronics behave - as you can see from even this simple problem.

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#### shteii01

Joined Feb 19, 2010
4,644
Sorry to niggle, but you shouldn't report an answer to 3 digits when you have rounded pi to just two in your calculations.
My calculator uses 9 decimal places for pi. I am lazy to type on internetz, but I am not lazy to use high precision of my calculator.

#### shteii01

Joined Feb 19, 2010
4,644
"I dont know if there is a better way than to look at the answer and muck about with it. i dont feel like i have understood the question or how to do it.....because i havent and i cant."

Yes, there is a better way: first learn algebra and trigonometry, then electronics. You can't pursue a serious course in electronics by mucking about with trial and error to match given solutions in a text. The skills you need are at least a basic understanding of the applicable physics and basic high school math. These are quite useful even for an electronics hobby, but for pursuit of a career they are essential.
First let me tell you that ninja is really annoying to me, probably for the same reasons you listed. So I understand your sentiment.

However. If, big if here. If ninjaman really following book solutions when he does examples... Then those solutions should provide a sort of step by step list of what to do and in what order to do it. So. On one hand they should be able to simply follow the steps. On the other hand, I have encountered textbooks that when providing example solutions, skip steps. I hate those books with a passion. There were a couple of times I was ready to tear my hair out, that is how frustrated I was because I just could not see how a solution to example problem jumped from point in the solution to the next.

#### ninjaman

Joined May 18, 2013
341
shteii01 PLEASE DONT RESPOND TO MY POSTS, IF I AM ANNOYING YOU PLEASE GET LOST!!!

#### bertus

Joined Apr 5, 2008
22,275
Hello Simon,

What kind of troubles do you have with @shteii01 ?
He is only trying to point you in the right direction.

My calculator (KCalc on my OpenSuse PC) can be set to any number of digits.
Pi in 24 digits gives 3,14159265358979323846264 on it.

Bertus

#### WBahn

Joined Mar 31, 2012
30,034
First let me tell you that ninja is really annoying to me, probably for the same reasons you listed. So I understand your sentiment.
@shteii01: This is really uncalled for -- or at the very least could have been stated a lot more softly. Remember, this is his thread and there is no requirement for you to even read it, let along respond to it.

#### WBahn

Joined Mar 31, 2012
30,034
dteremine the frequency and periodic time for an alternating emf having an instantaneous voltage of 5v, 0.02 seconds after passing through zero if the peak value is 12v.
there are examples in the book that i looked at that gave me some idea. i wrote out the formula like this
5v = 12v sin(2pi * ? * 0.02), i tried to rearrange this and got 3.324 which is close to the answer. divide everything by 5 except what i dont have, the frequency.
then i looked at an example
5/12 = 0.416, this inverse sin 0.416 = 0.42977 (rad) which is getting somewhere closer i think. convert this to degrees to get 24.62, put this in 12vsin(24.62) = 4.99volts. so 0.42977 has something to do with the answer. after mucking around i got 0.42977/ 2pi * 0.02 = 3.42 Hz which is close and 1 / 3.42 = 0.29

I dont know if there is a better way than to look at the answer and muck about with it. i dont feel like i have understood the question or how to do it.....because i havent and i cant.

In most cases, the electronics/physics is the easy part -- it's the math that is involved. This problem is a prime example:

Physics/Electronics: The mathematical representation for a sinusoidal waveform is:

$$v(t) \; = \; V_p \, \sin \(2 \pi f t$$
\)

There. That's all there is to the physics and/or the electronics. The rest is pure mathematical manipulation to solve for f when everything else is known. You will be forever critically handicapped until you make the decision to learn the necessary math.

For this problem, these steps look like the following:

$$v(t) \; = \; V_p \, \sin \(2 \pi f t$$
\frac{v(t)}{V_p} \; = \; \sin $$2 \pi f t$$
\sin^{-1} $$\frac{v(t)}{V_p}$$\; = \; \sin^{-1}$$\sin \(2 \pi f t$$ \)
\sin^{-1} $$\frac{v(t)}{V_p}$$\; = \; 2 \pi f t
2 \pi f t \; = \; \sin^{-1} $$\frac{v(t)}{V_p}$$
f \; = \; \frac{\sin^{-1} $$\frac{v(t)}{V_p}$$}{2 \pi t}
\)

#### ninjaman

Joined May 18, 2013
341
Hello Simon,

What kind of troubles do you have with @shteii01 ?
He is only trying to point you in the right direction.

My calculator (KCalc on my OpenSuse PC) can be set to any number of digits.
Pi in 24 digits gives 3,14159265358979323846264 on it.

Bertus
I have had similar posts from him. he gets annoyed at my lack of ability. that is his problem and should be kept to himself. i understand that when i post a question to include as much information as i can along with my attempt. i dont believe he is in anyway required to post a reply, if he does it would be nice if he remembered that maybe others pick things up slower, others may not be attending school or have as much education as the responder. i have an issue with learning, i dont believe that i should change career choice as a result of slightly upsetting any of you by asking questions. i do things the way i do because trying to learn something that i can not visualize is tricky. i am making an effort to learn algebra and trigonometry. you can not see this effort. my ability to understand a question written in a text book doesnt mean that i am not hard working or focused. most of my recent education has been completed mostly on my own. btec level 3 electrical installation through distance learning, hnc through college with a crap lecturer, i completed the course through distance learning as the lecturer was making things harder for me. recently as uni i was getting a distinction until i dropped out. the reason was because of the money and that i felt i wasnt getting the support i required. not to mention the lecturers were useless. any lecturer reading this would most likely think that i am lazy, i would say that i was putting in the effort and most lecturers want an easy life. i found most of the lecturers to be quite rude. i got 100% on my programming tasks and over 70% in everything else.

#### WBahn

Joined Mar 31, 2012
30,034
i have an issue with learning, i dont believe that i should change career choice as a result of slightly upsetting any of you by asking questions.
Agreed -- that, by itself, is not sufficient reason to change careers. But by the same token we all need to realize that there are things that are easy for us, things that are difficult but doable for us, and things that are not doable with any reasonable amount of effort, no matter how much we might want to pursue that particular path. It will be up to you to decide if and when this path crosses that threshold -- just do yourself a favor and acknowledge, to yourself, that such a threshold does exist and be on the lookout for it.

#### shortbus

Joined Sep 30, 2009
10,045
Why single out only Shteii01? DGElder was the first(in this thread) to tell him the same thing.

#### WBahn

Joined Mar 31, 2012
30,034
Why single out only Shteii01? DGElder was the first(in this thread) to tell him the same thing.
Very different tone of voice (of keys?). Also, Simon's reaction wasn't so much at being told that he needs to focus on improving his math, it was more to being told by someone choosing to take the time to respond to his thread that they found him annoying (Simon can correct me if I'm wrong). I also don't think that Shteii01 was meaning to be as insulting as he came across, given the content of the rest of his post.