Hi, i have an equation in the form of what is the square root of this equation? the solutions says , but im not sure how to get this. tia
It looks like that is an approximate solution for the case where B is much greater than C. Note, I'm assuming that C(t)=Ccos(wt). To see this, square the solution, as follows. Take the case where B is 10 times greater than C. In this case the order of magnitude of B squared is 100, the order of magnitude of C(t) is 1 (or less) and the order of magnitude of C(t)/(2B) squared is 0.0025 (or less). This means the last term can be neglected in many practical cases, provided the assumption that B>>C is met (note that the double greater than sign >> means "much greater than").
Perhaps you understand the half a question better than I did Steve. Please tell? As a matter of interest if you take the B^2 to the other side and factorise you get (A-B) (A+B) = Ccos(wt) which leads to t = arccos {(A-B) (A+B) /C }/w
It's just a supposition on my part as to what the question really is, but the answer looks like the first two terms of the binomial expansion with power of 1/2. There is no way that that answer can be exact, and the type of approximation I mentioned is somewhat common in physics and engineering, but typically is unacceptable in a pure math context. I hope the source of the solution makes it clear that there is an approximation involved. A good approximation to know by heart is , where it is assumed that ε<<1. This can be used in the following way, in this case.
EDIT: figured it out, thanks again Hello steveb, could you clarify in that last step how you went from it looks like you divided everything under the square root by B^2 but then how did a B appear outside of the square root? thanks again
Hi, to sort of add onto this problem, I am wondering how I can find the amplitude of a sin wave at multiple frequencies. As an example, When you plot this, it gives a single sinusoid, but im not sure how i can calculate the amplitude of that waveform thanks As a visual example, i plotted three sinusoids with the same amplitude but varying frequencies. I cant seem to get a grasp of how i would determine the amplitude of the red plot http://imgur.com/YZq85