Task 2

Scenario: In the electrical circuit design and analysis, there is an unbalanced, three-phase, star-connected, electrical network. If we consider three closed loop network with Kirchoff’s Voltage Law, we can get the simultaneous equations as follows:

2.4 I1 + 3.6 I2 + 4.8 I3 = 1.2

 -3.9 I1 + 1.3 I2 – 6.5 I3 = 2.6

 1.7 I1 + 11.9  I2 + 8.5 I3 = 0

Task 2.1 (P2.1)

Construct the above algebraic equations to represent the engineering problems in matrix form.

Task 2.2 (P2.2)

Solve the above simultaneous linear equations for I1 , I2 and I3 by using matrices and determinants.

Task 2.3 (P2.3)

Given that the critical speeds of oscillation, lambda , of a loaded beam are given by the non-linear equation 

Solve the non-linear equation by Newton’s method, correct to 4 decimal places, to determine the values of lambda.