230 Higher Engineering Mathematics
- Ifz=7ej^2.^1 , determine lnz(a) in Cartesian
form, and (b) in polar form.⎡
⎣(a)ln7+j 2. 1
(b) 2. 86 ∠ 47. 18 ◦or
2. 86 ∠ 0. 82⎤
⎦- Given z=4e^1.^5 −j^2 , determine lnzin polar
form. [3. 51 ∠− 34. 72 ◦or 3. 51 ∠− 0 .61] - Determine in polar form (a) ln( 2 +j 5 )
(b) ln(− 4 −j 3 ) ⎡
⎢
⎢
⎣(a) 2. 06 ∠ 35. 26 ◦or
2. 06 ∠ 0. 615
(b) 4. 11 ∠ 66. 96 ◦or
4. 11 ∠ 1. 17⎤
⎥
⎥
⎦- When displaced electrons oscillate about an
equilibrium position the displacementx is
given by the equation:
x=Ae{
− 2 htm+j√
( 4 mf−h^2 )
2 m−a t}Determine the real part ofx in terms oft,
assuming (4mf−h^2 ) is positive.
[
Ae−ht
2 mcos(√
( 4 mf−h^2 )
2 m−a)
t]