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Document Preview: Find the Laplace transform of . Find the Laplace transform of . Find the Laplace transform of . Find the Laplace transform of Find the Laplace transform of Find the inverse Laplace transform of .Find the inverse Laplace transform of Find the inverse Laplace transform of Consider the following initial value problem: Using for the Laplace transform of , i.e., , find the equation you get by taking the Laplace transform of the differential equation and solve for Find the Laplace transform of Find the Laplace transform of Find the inverse Laplace transform of Find the Laplace transform of .Take the Laplace transform of the following initial value problem and solve for : . Now find the inverse transform to find Find the Laplace transform of Find the convolution of and     Let denote the Laplace transform of . Find . Now find the inverse Laplace transform to obtain NOTE: Your answer will require the unit  HYPERLINK "http://webwork.math.ttu.edu/webwork2/s113mtodam3350sD01/HW6/18/?effectiveUser=moshahid&displayMode=images&showOldAnswers=1&user=moshahid&key=chV6GnJkoizIcJjSxoQacVHVsGvt8s7Q" \o "Click to Continue > by Text-Enhance" step function     which in Evaluate the integral (here is the Dirac delta function)   ANS:   Find the Laplace transform of the given function

Robert · Accepted Answer

Sol: (1)
       
   
5
6 2
2 sin 3
20
2 6 3
9
t
L f s L L L t
L f s
s s s
 
        
 
   


Sol: (2)
     
   
       
   
   
2
2
2
3 2
3 2
1
1 2
1 2
2 1 2
2 2 1
L f s L t
L f s L t t
L f s L t L L t
L f s
s s s
L f s
s s s
  
 
    
    
  
  
 
Sol: (3)
     
     
   
2
2
2
4cos 2 3
4cos 2 3
4 3
4 2
t
t
L f s L t e
L f s L t L e
s
L f s
s s
   
      
 
 

Sol: (4)
     
     
   
   
   
   
   
1
0
1 1
0 0
1 1
1
0
0 0
1 1 1
2
0 0 0
2 2
2 2
1
1 1
1 1
st
st st
st st st
st st st
s s s
s
L f s L f t
L f s e t dt
L f s te dt e dt
te e e
L f s dt
s s s
te e e
L f s
s s s
e e e
L f s
s s s s s
e
L f s
s s s

 
  
  
  

   
 
 
   
     
    
     
       
       
    

   

 


Sol: (5)
     
     
   
   
   
2
0 2
2
2 2
0
2
2
0 2 2
2
2
0 2 2
2
2
2
st st
st
st st
st st st st
st st st st
L f s L f t
L f s e dt e t dt
e
L f s te dt e dt
s
e te e e
L f s dt
s s s s
e te e e
L f s
s s s s

 

 
 
 
   

 
   
   
  
 
   
 
     
        
       
       
         
          
 
 

   
   
   
2
2 2 2 2
2
2 2 2
2
2
2
1 2
1
1
s s s s
s s s
s
e e e e
L f s
s s s s s
e e e
L f s
s s s s
e
L f s
s s

   
  


 
      
 
    
 
 
Sol: (6)
   
   
   
   
1
2
1 1
2 2
1 1
2 2
6
9
6
9 9
3
2
9 9
cos3 2sin 3
s
y t L
s
s
y t L L
s s
s
y t L L
s s
y t t t

 
 
 
   
   
        
   
        
 

Sol:

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