Hello guys, I am newbie here, and this id my first post. Somebody suggested me to ask my question here. Sorry but I have some problems calculating the the derivatives and integrals of sine waves in forms of sin^2 wt. I have a circuit which it's input has the form of "Vmsinwt" I added a dc offset to it as Vdc, So the final input has the forms of (Vdc + Vmsinwt). The output of my circuit when the input signal is as (Vdc + Vmsinwt) would be in forms of (Vc + Vmsinwt) where Vc is the peak amplitude of a sine wave too which of course is just equal to Vdc. Now I want to square the said ouput and then take double derivative of it. By squaring, we'll get this: (Vc + Vmsinwt)². But I can not go on to take this: δ²/δt² (Vc + Vmsinwt)² . I just can take the derivative for sinx and cosx, Not for Vmsin² wt. So plz kindly can you help me out HOW to do it? what is the method of doing so and whats the result plz? What if the input happens to be Vmcoswt? Thanks a bunch
Is this homework? Why do you want to calculate the second derivative? In general the following is true:
you are differentiating with respect to t. everything else is considered constant so first derivative is: δ/δt (Vc + Vmsinwt)²= 2 (Vc + Vmsinwt)*Vm*cos(wt)*w then second derivative is: δ/δt [2 (Vc + Vmsinwt)*Vm*cos(wt)*w]= δ/δt [2w*Vm*Vc*cos(wt)+w*Vm²*2*sinwt*coswt]= δ/δt [2w*Vm*Vc*cos(wt)+w*Vm²*sin(2*wt)]= 2*w²*Vm*Vc*(-sin(wt))+w²*Vm²*cos(2wt2)*2
lookup 'chain rule'. it helps differentiating more complex terms like sin²(wt) δ/δt sin²(wt) =2*sin(wt) * δ/δt sin(wt) =2*sin(wt) * cos(wt)*δ/δt (wt) =2*sin(wt) * cos(wt)*w =sin(2wt)*w you can also lookup wolfram alpha and bookmark it... you will need it
Hi Panic, Thank you very much for your reply. Please can you let me know How did you calculate the above? Can you Explain this too plz? Are you sure regarding to the final response? Do'nt you think that it needs a thirs component?
The thread has been moved to the Math section, since the OP doesn't respond whether this is homework or not.
He's been corresponding with me by PM. I encouraged him to post his questions on the forum, for the benefit of him and the members. From what he said, this is not homework. It is a small part of a very ambitious project, which I will leave to him to disclose if he so wishes.
Actually my question is not a homework, I just want to know the response of my question because The output of my circuit has such a square then doble derivative response, And I want to know how it does look like. Yet I am wondering why by derivation of (Vc + Vmsinwt)² we will reach to this!: δ/δt (Vc + Vmsinwt)²= 2 (Vc + Vmsinwt)*Vm*cos(wt)*w Can you guys plz help me out and enlighten me.
It has already been explained to you that it's an application of the chain rule. This is taught in every beginning calculus class, but it sounds like you haven't taken calculus. The basic principle is that when you have a function of a function (sometimes called function composition), the derivative of the composite function can be calculated using the chain rule. This is what the people above used to do the calculation. I'm sure it looks mysterious when you first see it, but after working through some examples in a calculus text it becomes second nature. I'll refer you to a calculus text or the web. One good place to learn about it is here: http://www.khanacademy.org/#browse. Go to the calculus section and look at the chain rule videos.
Thanks I already knew about chain rule, But I have a small scale experience regarding to that. Thats why I couldnt do it my self. Anyway I guess that this is not true: δ/δt (Vc + Vmsinwt)²= 2 (Vc + Vmsinwt)*Vm*cos(wt)*w Are you agreed with me?
yep, he has trouble with differentiation... here is link to interesting math site with plenty of videos explaining everything pretty well. there are several videos on chain rule: http://patrickjmt.com/ hope that helps