a.   The two alternating voltages are given by v_1=15 sinωt volts and v_2=25 sin?(ωt-π/6)volts.  

i. Determine a sinusoidal expression for the resultant v_R=v_1+v_2 by finding the horizontal and   vertical components.

ii.  Determine the resultant v_R=v_1-v_2 using horizontal and vertical components.

(b)Calculate the 1^st and 2^nd  moment  of area for the shape shown about the axis s-s and find the position of the centroid.       ( Part of L.O. 3.1)

L.O. (Part of 3.1)

(c) Find the eigenvalues and eigen vectors for the matrix

0  2  1

4  1   0

4  0   1

TASK: 5

A. Determine the power series solution of the differential equation:

(d^2 y)/?dx?^2 +x dy/dx+2y=0  Using Leibniz - Maclaurin’s method, given the boundary conditions that at

x=0,y=1  and  dy/dx=2      (L.O.4: 4.4)

TASK 6:

A. Determine the general power series solution of Bessel’s equation.        

x^2  (d^2 y)/?dx?^2 +x dy/dx+(x^2-v^2 )y=0

                                                                        (Part of D3)

B.    Show that the power series solution of the Bessel equation of the above problem  may be written in terms of the Bessel functions

Attachment:- assignment 2.docx