Fourier Transforms

1.    If  and  , use the Fourier Transform properties to determine the following.

2. Use the Fourier Transform tables and properties to determine the following.

3.    Prove that the trigonometric, complex exponential and Cosine with phase form of Fourier series are equivalent and derivable from each other.



4.    Using trigonometric form Find the Fourier series of:



 And derived the same results using complex exponential form.



5.    Prove that the integral:

6.    Define the Fourier and inverse Fourier Transforms and Prove that the Fourier transforms are a special case of Laplace Transforms.




7.    Find the Fourier Transforms of the following signals:







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Laplace Transforms

All these exercises are solved step-by-step. Typed on MS word document.



1.    Define Laplace transforms. What is the motivation of using Laplace transforms in engineering?


2.    Find the Laplace Transforms of an exponential function

3.    Given a differential equation with initial condition y(0)=1:

a.    Solve using Laplace transforms.
b.    Find transfer function.

4.    In the following circuit, assuming that the initial capacitor voltage is zero and initial inductor current is zero.

a.    Determine the circuit transfer function H(s) from the input vin(t) to the output vc(t).for the values of the components shown in the figure.

b.    Determine the time response vc(t) of the circuit if  , i.e. 1.2 impulse input.



5.    Determine the Laplace transform of the following signals.



6.    Determine the Laplace transform of.



7.    Determine the inverse Laplace transform of  . Use tables and the MATLAB symbolic ilaplace() functions as necessary.



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Electric Field Near a Two Parallel Straight Line Charge

2平行直線電荷に近い電界


We show the electric field near a Two Parallel Straight Line Charge.

We have used the electric field strength E and the superposition principle to calculate the image below...

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eField.c is the code written in Language C using OpenGL library.

C Programming Assignment: N Body Simulation

We solved the N Body problem using C Programming Language and OpenGL library. A complete solution is available in request...

nBody.c

Three spring-mass system with collision: Written in C/C++ and OpenGL.

The full implementation is available on BUY NOW BUTTON...

threespring.c

Kruskal's and Prim's Algorithm: Implementation written in language C.

Algorithms for determining a minimal spanning tree for connected, non-directed, weighted graph, it is available on BUY NOW BUTTON...

 
Implementation of Kruskal's Algorithm is available, written in language C, furthermore you can compare it against Prim's Algorithm, also available.
 

Kruskal and Prim Algorithm

Minimmum spanning tree.

Minimal spanning tree weight = 66

kruscal.c   and    prim.c

Kirchhoff's law

In the circuit shown in Figure A, all resistors are 8 Ω, and the internal resistance of each battery is 3 Ω. Other parameters are shown on the circuit diagram.

a) Determine the values of the currents that flow through each resistor R1, R2, R3, and R4.
The directions of the current through each resistor should be indicated by arrows on the circuit diagram.

b) Determine the reading of a voltmeter connected between the points A and B.

c) Determine the amount of charge accumulated on the capacitor C1. What is the sign of the charge on the left-hand-side plate of the capacitor?

We have solved all questions above. Please click on BUY NOW in order to download all steps solutions.

For example...