Higher Engineering Mathematics, Sixth Edition
602 Higher Engineering Mathematics (i) L { d^2 y dx^2 } − 3 L { dy dx } =L{ 9 } Hence [s^2 L{y}−sy( 0 )−y′( 0 )] −3[sL{y}−y( 0 ) ...
The solution of differential equations using Laplace transforms 603 Whens= 0 ,− 120 =− 20 A, from which,A=6. Whens= 5 , 180 = 45 ...
604 Higher Engineering Mathematics In Problems 2 to 9, use Laplace transforms to solve the given differential equations. 9 d^2 ...
Chapter 65 The solution of simultaneous differential equations using Laplace transforms 65.1 Introduction It is sometimes necess ...
606 Higher Engineering Mathematics L { dx dt } −L{y}+ 4 L{et}=0(2) Equation (1) becomes: [sL{y}−y( 0 )]+L{x}= 1 s (1′) from equa ...
The solution of simultaneous differential equations using Laplace transforms 607 Problem 2. Solve the following pair of simultan ...
608 Higher Engineering Mathematics i.e. 3 s^2 −s− 2 =A(s+ 2 )(s− 1 ) +Bs(s− 1 )+Cs(s+ 2 ) When s=0,− 2 =− 2 A, hence A= 1 When s ...
The solution of simultaneous differential equations using Laplace transforms 609 Using the procedure: (i) [s^2 L{x}−sx( 0 )−x′( ...
Revision Test 18 This Revision Test covers the material contained in Chapters 61 to 65.The marks for each question are shown in ...
Chapter 66 Fourier series for periodic functions of period 2π 66.1 Introduction Fourier seriesprovides a method of analysing per ...
612 Higher Engineering Mathematics f(x)=a 0 + ∑∞ n= 1 (ancosnx+bnsinnx) (1) where for the range−πtoπ: and a 0 = 1 2 π ∫π −π f(x) ...
Fourier series for periodic functions of period 2π 613 From Section 66.3(i): a 0 = 1 2 π ∫π −π f(x)dx = 1 2 π [∫ 0 −π −kdx+ ∫π 0 ...
614 Higher Engineering Mathematics x f(x) f(x) P 1 0 (a) (b) (c) 4 24 2 2 /2 2 /2 x f(x) f(x) 4/3 sin 3x 2 2 /2 0 2 ...
Fourier series for periodic functions of period 2π 615 = 5 2 π {[ −cos [ 2 π ( 1 2 +n )] ( 1 2 +n ) − cos [ 2 π ( 1 2 −n )] ( 1 ...
616 Higher Engineering Mathematics For the waveform shown in Fig. 66.6 deter- mine (a) the Fourier series for the functionand ( ...
Chapter 67 Fourier series for a non-periodic function over range 2π 67.1 Expansion of non-periodic functions If a function f(x)i ...
618 Higher Engineering Mathematics x f(x) f(x) 52 x 22 2 0 22 2 2 3 Figure 67.2 From Section 66.3(i), a 0 = 1 2 π ...
Fourier series for a non-periodic function over range 2π 619 x f(x) f(x) 5 x 22 2 0 2 3 Figure 67.3 It is more conven ...
620 Higher Engineering Mathematics and phase angle, α=tan−^1 ⎛ ⎜ ⎝ − 2 32 π 1 3 ⎞ ⎟ ⎠ =− 11. 98 ◦ or − 0 .209radians Hence the t ...
Fourier series for a non-periodic function over range 2π 621 Whenθ=π, f(θ )=π^2 Hence π^2 = 4 π^2 3 + 4 ( cosπ+ 1 4 cos2π + 1 9 ...
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