The Laplace transform of a function of time f(t) is a function of a new variable s and is designated...

Question

The Laplace transform of a function of time f(t) is a function of a new variable s and is designated as (1) u(t — s) (2) o(s) (3) F(s) (4) C"
2. Which of the following is the definition of the Laplace transform of f(t)?
(1) 2[ f(t)] = F(s) = (2)s—arn —1 r — 1 a"- (3) F(t) = „7-r. 1 f e"f(s)ds z 0-). (4) -C[fM] = 10 „.
14' f(t)e-"dt
3. The Laplace transform of the sum of several functions is (0)
to the sum of the individual transfo the product of several functions is (b) individual transforms. (1) (0) Equal, (b) equal (2) (a) Equal, (b) not equal
rms. The Laplace transform of to the product of the (3) (0) Not equal, (b) equal (4) (a) Not equal; (b) not equal

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promptly, Then Mail in this and all examinations as they are completed. start on rhe nexi lesson. l. The Laplace transform of a functiorr time of iis a function or a "f(t) variable new s and is designated as - - (l) (2) (3) (4) z(r s) d(s) r(s) e-" ) Which of the followine is the definition of the Lap place transform orf f(t)? F l* :F(s): (1) dt 8,1_f(t)l f(t)r-" I .'/ o ,nl - (2) s sL2 r-I t fo+j- (3)F(r):= e"f(s)ds | ZirJ J _t. a : (4) ',:,-f(t)r +l; J a 1 The Laplace transform of the sum of several functior cns is (o)- to the sum of the individual transfo place rf rms. The Lap transform o the product of (u) several functions is _to the t product thr ri e of individual transforms. (l) Equal, (3) equal Not equ ual, equal t.l 1u1 r"i 6i (2) Equal, not equal (4) Not equ ual; not equaI t"l 1uy r.l 1uy4. What = is theLaplace transform of 20u(t)1 I 63p f(t) 2A = (l) F(s) : 20 (3) F(s) S' 20 = (2) = F(s) (4) F(s) .t s+20 = 5. What is the Laplace transform of 3 e-2"t. f(t) -2 ,l : (l) 1 = F(s) (4) F(s) JS J 3 : = (2) F(s) (5) F(s) h t+2 1 = (3) F(s) r+3 6. Determine : - the Laplace transform (2t ot l0 sin 30'). f(t) -5s-+ 20 17.32 (l) : : r(s) (3) F(s) \/-\-' (s+2)2+4 s'+4 20 cos 30" : (2) F(s) (4) F(s)=ffi s2+4 of 7. What is the Laplace transform dt? f(t) I v0 - (3) (1) F(s t) sF(s) + /(0) r(s) (2) e-^F(s) 141 s 3-f,. * = (s) (s) 8. Let G Find the limiting value of G as r approaches it |-e-" zero. (Hint: Use L'Hopitals Rule, Lesson 6216; Topic 5-3; Guideline 2.) : (l) lim 4 G(s) J+U = (2) c(s) 3 lE = (3) 2 G(s) lg = (4) G(s) l.s lE 9. Determine the transform of the periodic waveform shown in Fig. E- l. \a ) re-* (Hint: Problem 5-32 (r)F(s):hft and example 2-L7 in Lesson 6420) (2) = F(s) ,2o , *l 1n'-*, .s-*r- 7]rs-*r- +2n : (3) F(s) *l;F nrt \=. ),e- : (a) r(s) *l;FI I I Fig. E-l I -"nis : 10. A voltage v(t) Ltze passed through a delay line having a delayof 4 sec....

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Robert · Accepted Answer

1. The Laplace transform of a function of time  f t  is a function of a new variable s and is 
designated as  F s . 

2. The definition of the Laplace transform of  f t  is 
 
     
0
.stf t F s f t e dt

    L
3. The Laplace transform of the sum of several functions is equal to the sum of the 
individual transforms. The Laplace transform of the product of several functions is not 
equal to the product of the individual transforms.
4. The Laplace transform of    20f t u t  is given by 
 
   
 
 
0
0
0
0
20
20
20
20
.
st
st
st
st
F s f t e dt
u t e dt
u t e dt
e dt
s


















5. The Laplace transform of   23 tf t e  is given by 
 
   
 
0
2
0
2
0
3
3
3
.
2
st
t st
s t
F s f t e dt
e e dt
e dt
s



 

 









6. The Laplace transform of    10sin 2 30f t t    is given by [1] 
 
   
 
 
 
   
0
0
0
0
2 2
2
2
10sin 2 30
10 sin 2 cos30 cos 2 sin 30
5 3 sin 2 cos 2
5 3 sin 2 5 cos 2
2
5 3 5
4 4
5 10 3
4
5 17.32
.
4
st
st
st
st
F s f t e dt
t e dt
e t t dt
e t t dt
t t
s
s s
s
s
s
s









  
  
 
 
   
    
    
 


 






L L

7. The Laplace transform of  
 
   
0
t
g t f u du 
  is given by
   
   
    
   
 
 
0
0
0
0
0
1
1 1
1 1
0 0
0
.
st
st
st st
t
st
G s g t e dt
g t d e
s
g t e e d g t
s s
g f t e dt
s s
F s
s
F s
s






 




 
    
     
 






8. We are given the function 
 
 
2
2
3
.
1 s
s s
G s
e




 We wish to compute  
0
lim .
s
G s


 Using L’Hopital’s rule, we obtain
    20 0
2 3 3
lim lim 1.5.
2 2ss s
s
G s
e 
 
   
 

9. We wish to find the Laplace transform of the periodic waveform shown below: 
 
 
 
 We have
         2sin 2 2 1 ,
n
f t t u t n u t n


      
 whence
   
     
 
   
   
   
0
0 0
2 1
0 2
2 1
0 2
2 1
0
2
2 1 2 12 2
2 sin 2 2 1
2 sin
1
1
1
st
st
n
n
st
n n
n
s i t s i t
n n
n
s i t s i t
n
t n
n s n sns ns
F s f t e dt
t e u t n u t n dt
t e dt
e e dt
i
e e
i s i s i
e e e e
i s i s
 
 


 










   


   


    

      

  
 
 
  
    
   
 
   


 
 

0
0
2 2
0
2 2
0
1 1 1
1
2
.
n
ns
n
ns
n
ns
n
i
e
i s i s i
s i s i
e
i s
e
s

 
 














 
 
 
 
  
  
   
  
 







10. A voltage   2 32 tv t t e is passed through a delay line having a delay of 4 s.

The Laplace transform of a function of time f(t) is a function of a new variable s and is designated as (1) u(t — s) (2) o(s) (3) F(s) (4) C" 2. Which of the following is the definition of the Laplace...

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