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In connection with Equation (16.31), I claimed that any function on the interval 0 ≤x ≤L can be expanded in a Fourier series containing just sine functions. This is at first sight very surprising since one is used to the claim that the general Fourier series requires sines and cosines. In this problem, you'll prove this surprising claim. Let f (x) be any function defined for 0 ≤ x ≤L. We can define a function f (x) for all x by setting it equal to the given function in the original interval and requiring that
for all x. Prove that this defines a function which is (1) periodic with period 2L, (2) odd, and (3) the same as the original f (x) on the original interval. Write down the ordinary Fourier expansion for this new f (x) and show that the coefficients of the cosine terms are all zero. This establishes the possibility of expanding the original function in terms of sines alone. 27Bearing in mind that the period of the new function is 2L, write down the standard formula (5.84) for the expansion coefficients and show that your answer agrees with (16.33). The Fourier sine series is especially convenient for discussing functions that are zero at the end points x = 0 and L.
Estimate the mass transfer area per unit volume (a) for this column, estimate the Hoy value for this column and calculate Noy and estimate the height of the column using your answer for Hoy
A tractor-trailer truck driver friend often delivers to companies that do not have a fork truck or loading dock. She wants to install a lift-gate on her trailer so she can load and unload her truck without a fork truck.
Determine the periods and find exponential fourier series coeffecients of functions. A.) f(t) = 2(cost)(cos2t) B.) g(t) = 3 + 2e^-j2t + 2e^j2t + 2cos4t C.) h(t) = 4
briefly explain your ideal job as electrical engineer? why did you select this career? what goals do you have in this
Time to failure in months, X Fx(x) = (1 - e ^(-x/5))u(x) for plant A Fx(x) = (1 - e ^(-x/2))u(x) for plant B Plant B produces three times as much as plant A. What is the probability that a bulb purchased at random will burn at least
The sinusodial modulating wave m(t) = (Am)cos(2*pi*fm*t) is applied to a phase modulator with sensitivity kp. The unmodulated carrier wave has frequency fc and amplitude Ac. Determine the spectrum of the resulting phase-modulated wave
Suppose you have 20 identical capacitors in a series RCLcircuit. All of these capacitors are in series. How many of these capacitors much be removed so the resonant frequency is cut inhalf
An induction motor has an output or shaft power of 30 kW at 86% efficiency. For this operatingcondition, stator copper loss = rotor copper loss = core loss = mechanical rotational losses. Determine the slip.
A 5-element uniform linear array with inter-element spacing of λ/2 is to have maximum radiation in the direction θ=60° , find the current phases , find the directions of null radiation , hence sketch the radiation pattern
Where x(t) is the input and y(t) is the output. a.] Find the impulse response h(t) of the average. Is the system causal b.] Let x(t) = u(t). Find the output of the average.
In the latest release of the game there are 8 characters the user can choose from. The user can choose one character from the 8 characters by moving the controller joystick up, down, left, or right. Each character has a 3 bit code that is sent to ..
The coil area is 2.7 mm*mm, the number of turns is 187; it also has an iron core with permeability mu= 600. How long must the coil be to have an inductance of 8.3 mH
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