FreeMat: Introduction to Numerical Computation

Solving Simultaneous Equations:

Assignment 1

To solve the system of equations derived from this circuit I used KCL and KVL. 

See the derivation and diagram below.

I created simple matrices with respect to current, voltage, and resistance in FreeMat to solve for the current across R_3.

Adding Sinusoids:

Assignment 1

1. Circuit A has a time constant of 100 ms, while circuit B  has a time constant of 200 ms. The circuit output is 2e^(-t/tau).

Circuit outputs generated by FreeMat were graphed for circuits A and B as the blue and green curves respectively.

From this graph it shows that circuit A reaches a lower output sooner.

2. If the circuit's output is related to 2(1-e(-t/tau)) the FreeMat generates the graph below.

In this case, circuit A-in blue-would also reach its maximum output sooner than circuit B.

Assignment 2

1. The output generated by the sum of two sinusoidal functions was found theoretically and through FreeMat. FreeMat also graphed the result of both methods to compare directly.

f1: blue

f2: green

F: red

This is the result of the theoretical function which matches exactly to that of the first method.

2. For a frequency of 10 Hz the process of plotting the graph was very similar except that the period is much shorter.