Sinusoidal function Definition and 20 Threads

The known expression of the wave function is where A is the amplitude, k the wave number and ω the angular velocity. The mathematical definition of arc length for a generical function in an interval [a,b] is where, in our sinusoidal case: For our purpose (calculation of the length in one...

I(k_x, k_y) = \int_{0}^{R} \int_{0}^{2\pi} J_{m-1}(\alpha \rho) \sin((m + 1) \phi) e^{j\rho(k_x \cos\phi + k_y \sin\phi)} \rho d\rho d\phi Is there any way to do it? J is the Bessel function of the first kind. I thought of partially doing only the phi integral as \int_{0}^{2\pi} \sin((m + 1)...

Homework Statement What is the derivative of ##f(x)=\frac {2x^2} {cos x}##? Homework EquationsThe Attempt at a Solution ##F(x)=\frac {2x^2} {cos x}## So... ##f(x)=2x^2## and ##f'(x)=4x## ##g(x)=cosx## and ##g'(x)=-sinx## If I plug these into the quotient rule I thought that I would get...

Homework Statement Hello! I am doing exercises on sinusoid functions from the beginning of Trigonometry. I hoped I understood the topic, but it seems not quite, because I don't get the results authors show as examples for one of possible answers, as there can be a few answers to the same...

Hi everyone, I am working on some problem relating to radars. The problem boils down to finding the frequency of the complex exponential in a constant + complex exponential + noise model. I found some papers on sinusoid recognition but they use the sinusoid + noise model only. I tried to come...

Homework Statement [/B] Consider an ideal rope where there is a wave moving at velocity ##v=20 m/s##. The displacement of one end of the rope is given by $$s(t)=0.1 \mathrm{sin}(6 t)$$ a) Find the wavefunction ##\xi(x,t)##, knowing that it is progressive b) Find the distance ##\delta## (in...

In Simple Harmonic Motion, can (k/m) = ω2 be expressed for all SHMs or only the ones in which the mass due to which the SHM is being executed is performing a circular motion? Since for example, in the case of spring, there is no circular motion involved, so omega should not be defined for...

Homework Statement Hi! I'm trying to find the points of intersection of a sinusoidal function and a line. The line is y=x/7. The function is y=sinx. Can someone tell me how to determine the number of intersections and exact intersections. I would also like to know if the same method can be...

I really need someone to break it down for me. I think I understand A and D, but I am confused on B and C. I have some example problems. But first, the equation my pre-calculus teacher has given us is y=Asin(2π/B(θ-C))+D. But I am still having a lot of trouble. Find amplitude, period, a phase...

Homework Statement For a sinusoidal function, how do you determine the highest value exceeded 10% of the time? The pink line in the attached pic indicates that value. Just wondering how you actually determine the value for a periodic function? Homework Equations The Attempt...

Here is the question: Here is a link to the question: One of the largest ferris wheel ever built is in the british airways london eye which was completed in 2000. T? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Find derivative of: h(x) = 3e^{sin(x+2)} Homework Equations chain rule of derivatives, product rule(?) The Attempt at a Solution I'm quite sure I'm doing this wrong. Because the exponent is a product, for the derivative of the exponent I would have to use the...

Hey forum, thanks in advance to anyone who can explain this to me! Homework Statement Find the derivative of each of the following: h(x) = 3e^sin(x + 2) The Attempt at a Solution My friend and I worked through this together and solved for: h’(x) = (3e^sin(x + 2))(cos(x + 2)) Using...

Homework Statement Measurements of the height h(t) of water in a harbor are recorded ,where h is measured in meters and t in hours.It was noted that the rise and fall of a tide is modeled by a sinusoidal function giving the height by : h(t)=a+bsin(kt+c). (a) Obtain values of the...

Question: 1. A clock is hanging on wall. length of minute hand is 16cm and the length is 8cm for the hour hand. The highest that the tip of the minute hand reaches above ground is 265cm. a) What is equation of axis, amplitude & period in minutes of function that represents the tip of hour...

Homework Statement Find the equation of the tangent to the curve y=2cos^3x at x=pi/3 Homework Equations The Attempt at a Solution y=2cos^3x dy/dx=-6sinxcos^2x 0=-6sinxcos^2x set x = pi/3 and solve for the derivative, plug the answer into y=2cos^3x where do I go from here...

I have seen many equations light as a wave but none of which have represented light as a simple sinusoidal function. I want to be able to graph light waves on a cartesian plane as one sine curve. I know that light isn't that simple but could light be represented as a 2 dimensional sine curve...

Homework Statement At the time of a full moon, the tides repeat with a period of about 12 hours, and the depth of water in a certain channel varies between 2 meters and 6 meters in a way that can be modeled by an equation of the form D(t) = A + Bsin(ct + d), where A is the average depth and...

In a sinusoidal function...suppose the value of δ is very large...then as x approaches any a, the value of f(x) might not approach L directly...or there should not be a direct relation; example - \lim_{x \to 1.5} sin x = 0.997494986 Where I've stated δ as 7...then if x = 1.5 – 6.9 =...

hello there, how do i solve over [0,2pi) for sin(2x)+sin(x)=0 thanks for what help you can give RansidMeat