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Question 44238

posted 10 months ago

Problem 6 One more chance for you folks who don't get MATLAB. Write me a live script that calculates the arc tan(x) for abs(x) <1.
\tan ^{-1} x=x-\frac{x^{3}}{3}+\frac{x^{5}}{5}-\frac{x^{7}}{7}+\cdots \quad=\sum_{m=0}^{\infty} \frac{(-1)^{m} x^{2 m+1}}{2 m+1}(-1 \leq x \leq 1)
The user should be prompted for x, and the script should check to see if abs(x) is <1 before proceeding. Then calculate the result until term< tol like u sual and display actual answer and the series answer. You just did this... I want to give a chance for those who couldn't do it last time.
Lets leave it at that. We also have a final next week.

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Question 44237

posted 10 months ago

\text { Easy one here Lets find the integral of } f(x)=(\sin (x)+\cos (x))^{2} \text { from } 0 \text { to } 4 \pi \text {. }
a) Use Simpsons rule on excel to do this numerically.
b) Optional.. try this by hand symbolically...
c) Do this both numerically and symbolically with MATLAB using built in functions. (this is 4lines of code!!)

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Question 44235

posted 10 months ago

For a tank draining problem with a constant feed rate, the governing equation is
\frac{d h}{d t}=\frac{Q}{A_{t}}-\frac{A_{t}}{A_{h}} \sqrt{2 g h}
Where Q is the flow rate in At is the tank area Ah is the hole area and h is the height in the tank. Lets say the hole diameter in 10 cm (watch your units) , the tank diameter is 1 m, Q is0.05 m3/sec, and g is 9.8066 m/s?. We will assume the initial height in the tank is 10 m and we can assume the tank is very tall (it wont overflow). Now don't get spooked by the problem.We want to use Euler's method to generate a table of h vs time. You will find this very similar to some examples I provided under "Euler". It should be easy to modify.
a) OK so set this up using Eulers method. Try a step size of 50 sec and run it out long enough to see what happens. (at least 5000 seconds).
b) At the point where the level becomes constant (it will) what is the flow rate out? (think .. this doesn't require a calculation.)
Add another column to use modified Euler with the predictor /corrector step.
Write a livescript program which asks the user for the flow rate in and the time duration., but has the other dimensions "built in" (that is just type dt=1, and dh =0.1, etc. Your livescript should generate an array of h vs t. Have the script plot h vs t. Just use straight Euler for this... not modified.

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Question 44236

posted 10 months ago

a) Conduction : Say we have a rod 1 m long which is at steady state. One end is 100 C,and the other is at 120 C. What is the temperature in the center?
b) OK again for a bar. The left hand temp To is 120 C. Then stepping to the right, the next"point" T1 is 115, the next T2 is 109, then T3 = 107 and so on to the end. Delta x is 0.1m

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Question 44234

posted 10 months ago

We have a function that you want to evaluate in MATLAB
f(x, y)=23 y^{\wedge} 2-3 x^{\wedge} 6+23
a) Write an anonymous function in MATLAB and write a livescript to ask the user to input xa nd then to input y and then have the function print out the answer
b) Have your livescript plot the value of f vs x from 0 to 10 for y = -2.

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Question 44233

posted 10 months ago

You want to make row vector "y" a column vector. To do so you could performy=y' or y=transpose(y).
in MATLAB z=sqr(4) will return 2
in MATLAB an IF and For statement may share the same end statement
MATLAB the following code would work to calculate sum of squares
The MATLAB operator <> is used to determine inequality between variables.
In MATLAB, if x is a matrixx.^2 is a valid statement
cos (60 degrees) is in fact 0.5 In excel cos(60) will give 0.5
Centered finite differences are more accurate than forward or backward finitedifferences.
In MATLAB, For, for, FOR are all equivalent

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Question 44519

posted 10 months ago

9. An infinitesimally thin metallic cylindrical shell of radius4.0 cm is centered on the z-axis and carries an evenly distributed current of 10.0 mA in the +az direction. (a)Determine the value of the surface current density on the
conductive shell and (b) plot H as a function of radial distance from the z-axis over the range 0 < 22< 12 cm.

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Question 44520

posted 10 months ago

10.An infinite length line carries current I in the +directional on the z-axis, and this is surrounded by an infinite length cylindrical shell (centered about the z-axis)of radius a carrying the return current I in the -azdirection as a surface current. Find expressions for the magnetic field intensity everywhere. If the current is 1.0A and the radius a is 2.0 cm, plot the magnitude of H versus radial distance from the z-axis from 0.1 cm to 4 cm.

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Question 44513

posted 10 months ago

3. : MATLAB: Consider a sphere with charge density Bv =120 nC/m3 centered at the origin with a radius of 2.00 m.Now, remove the top half of the sphere, leaving a hemisphere below the x-y plane. Find the electric field intensity at the point P(8.00m,0.00,0.00). (Hint: seeMATLAB 2.4, and consider that your answer will now have two field components.)

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Question 44515

posted 10 months ago

1. MATLAB: Suppose you have a segment of line charge of length 2L centered on the z-axis and having a charge distribution BL. Compare the electric field intensity at a point on the y-axis a distance d from the origin with the electric field at that point assuming the line charge is of infinite length. The ratio of E for the segment to E for the infinite line is to be plotted versus the ratio L/d usingMATLAB.

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