Question 1

Find the inverse Laplace transform of $$F ( s ) = \frac { 0.97 } { s \left( s ^ { 2 } + 0.8 s + 0.97 \right) }$$

Accepted Answer

$$f ( t ) = \left\{ 1 - e ^ { - 0.4 t } [ \cos ( 0.9 t ) + 0.4444 \sin ( 0.9 t ) ] \right\} u ( t )$$ clear all;
syms $t s$
$F = ( 0.97 ) / \left( s ^ { * } \left( s ^ { \wedge } 2 + 0.8 * s + 0.97 \right) \right)$
clear all;
syms ts
$E = ( 0.97 ) / \left( s ^ { * } \left( s ^ { \wedge } 2 + 0.8 * s + 0.97 \right) \right)$
$f = 1 l a p l a c e ( F )$
f=simplify(f)
pretty(f)
f = vpa ( f , 7 )
$f = 1$ laplace (E)
f=simplify (f)
pretty (f)
f =  vpa(f , 7 )

Question 2

Find the one-sided Laplace transform of $$f ( t ) = u ( - t + 8 )$$

Accepted Answer

$$F ( s ) = \frac { 1 } { s } - \frac { e ^ { - 8 s } } { s } = \frac { 1 - e ^ { - 8 s } } { s }$$

Question 3

Find the one-sided Laplace transform of $$f ( t ) = e ^ { - 2 t + 10 } u ( t - 4 )$$

Accepted Answer

$$F ( s ) = e ^ { 2 } \frac { e ^ { - 4 s } } { s + 2 }$$

Question 4

Find the initial value and the final value of f(t) if $$F ( s ) = \frac { s + 15 } { s ^ { 2 } \left( s ^ { 2 } + 4 s + 12 \right) }$$

Accepted Answer

\[\begin{array} { l } 
f \left( 0 ^ { +

Question 5

Find the one-sided Laplace transform of $$f ( t ) = e ^ { - ( t + 2.5 ) } u ( t + 2.5 )$$

Accepted Answer

The answer of Find the one-sided Laplace transform of \[f...

Question 6

Find the one-sided Laplace transform of $$f ( t ) = 7 \cos ( 3 t ) u ( t ) + 4 \sin ( 3 t ) u ( t )$$

Accepted Answer

The answer of Find the one-sided Laplace transform of \[f...

Question 7

Find the inverse Laplace transform of $$F ( s ) = \frac { 16 ( s + 1 ) } { ( s + 2 ) \left( s ^ { 2 } + 4 s + 20 \right) }$$

Accepted Answer

@#LAT-DLM& 
clear al

Question 8

Find the one-sided Laplace transform of $$f ( t ) = u ( t ) - 3 u ( t - 2 ) + 7 u ( t - 5 ) - 4 u ( t - 7 )$$

Accepted Answer

The answer of Find the one-sided Laplace transform of \[f...

Question 9

Find the inverse Laplace transform of $$F ( s ) = \frac { 3 s + 25 } { ( s + 5 ) ^ { 2 } ( s + 7 ) }$$

Accepted Answer

@#LAT-DLM& 
clear al

Question 10

Find the one-sided Laplace transform of $$f ( t ) = 5 \sin \left( 2 t - \frac { \pi } { 4 } \right) u ( t )$$

Accepted Answer

\[\begin{array} { l } 
f ( t ) = 5 \sin

Question 11

Find the initial value and the final value of f(t) if $$F ( s ) = \frac { s + 12 } { s \left( s ^ { 2 } + 2 s + 8 \right) }$$

Accepted Answer

\[\begin{array} { l } 
f \left( 0 ^ { +

Question 12

Find the one-sided Laplace transform of $$f ( t ) = t u ( t ) - 2 ( t - 2 ) u ( t - 2 ) + 6 ( t - 5 ) u ( t - 5 ) - 8 ( t - 7 ) u ( t - 7 ) + 4 ( t - 8 ) u ( t - 8 )$$

Accepted Answer

The answer of Find the one-sided Laplace transform of \[f...

Question 13

Find the inverse Laplace transform of $$F ( s ) = \frac { 2 s + 5 } { s ^ { 2 } + s + 1.06 }$$

Accepted Answer

@#LAT-DLM& clear all;
syms t s

Question 14

Find the one-sided Laplace transform of $$f ( t ) = ( t + 3 ) u ( - t + 6 )$$

Accepted Answer

The answer of Find the one-sided Laplace transform of \[f...

Question 15

Find the inverse Laplace transform of $$F ( s ) = \frac { s ^ { 2 } + 6 s + 18 } { s ( s + 3 ) ( s + 7 ) }$$

Accepted Answer

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f ( t ) = \left(

Question 16

Find the one-sided Laplace transform of $$f ( t ) = e ^ { - 2 ( t + 1.5 ) } u ( t + 1.5 )$$

Accepted Answer

The answer of Find the one-sided Laplace transform of \[f...

Question 17

$$\text { Let } \mathrm { f } ( \mathrm { t } ) = 2 \cos ( 5 \mathrm { t } ) \mathrm { u } ( \mathrm { t } ) \text {. Find the one-sided Laplace transform of } \mathrm { f } ( \mathrm { t } ) , g ( t ) = \frac { d f ( t ) } { d t } \text {, and }$$ $$h ( t ) = \frac { d ^ { 2 } f ( t ) } { d t ^ { 2 } }$$

Accepted Answer

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\mathrm { f } ( 0

Question 18

Find the inverse Laplace transform of $$F ( s ) = \frac { 6 s + 15 } { ( s + 3 ) ^ { 2 } ( s + 5 ) ^ { 2 } }$$

Accepted Answer

@#LAT-DLM& 
clear all;
syms @#LAT-DLM&
@#LAT-DLM&

Question 19

$$\text { Let } \mathrm { f } ( \mathrm { t } ) = 2 \mathrm { u } ( \mathrm { t } ) - 2 \mathrm { u } ( \mathrm { t } - 6 ) \text {. Find the one-sided Laplace transform of } \mathrm { f } ( \mathrm { t } ) , g ( t ) = \frac { d f ( t ) } { d t } \text {, and }$$ $$h ( t ) = \frac { d ^ { 2 } f ( t ) } { d t ^ { 2 } }$$

Accepted Answer

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\mathrm { g } ( \

Find the inverse Laplace transform of $F ( s ) = \frac { 0.97 } { s \left( s ^ { 2 } + 0.8 s + 0.97 \right) }$

Find the one-sided Laplace transform of $f ( t ) = u ( - t + 8 )$

Find the one-sided Laplace transform of $f ( t ) = e ^ { - 2 t + 10 } u ( t - 4 )$

Find the initial value and the final value of f(t) if $F ( s ) = \frac { s + 15 } { s ^ { 2 } \left( s ^ { 2 } + 4 s + 12 \right) }$

Find the one-sided Laplace transform of $f ( t ) = e ^ { - ( t + 2.5 ) } u ( t + 2.5 )$

Find the one-sided Laplace transform of $f ( t ) = 7 \cos ( 3 t ) u ( t ) + 4 \sin ( 3 t ) u ( t )$

Find the inverse Laplace transform of $F ( s ) = \frac { 16 ( s + 1 ) } { ( s + 2 ) \left( s ^ { 2 } + 4 s + 20 \right) }$

Find the one-sided Laplace transform of $f ( t ) = u ( t ) - 3 u ( t - 2 ) + 7 u ( t - 5 ) - 4 u ( t - 7 )$

Find the inverse Laplace transform of $F ( s ) = \frac { 3 s + 25 } { ( s + 5 ) ^ { 2 } ( s + 7 ) }$

Find the one-sided Laplace transform of $f ( t ) = 5 \sin \left( 2 t - \frac { \pi } { 4 } \right) u ( t )$

Find the initial value and the final value of f(t) if $F ( s ) = \frac { s + 12 } { s \left( s ^ { 2 } + 2 s + 8 \right) }$

Find the one-sided Laplace transform of $f ( t ) = t u ( t ) - 2 ( t - 2 ) u ( t - 2 ) + 6 ( t - 5 ) u ( t - 5 ) - 8 ( t - 7 ) u ( t - 7 ) + 4 ( t - 8 ) u ( t - 8 )$

Find the inverse Laplace transform of $F ( s ) = \frac { 2 s + 5 } { s ^ { 2 } + s + 1.06 }$

Find the one-sided Laplace transform of $f ( t ) = ( t + 3 ) u ( - t + 6 )$

Find the inverse Laplace transform of $F ( s ) = \frac { s ^ { 2 } + 6 s + 18 } { s ( s + 3 ) ( s + 7 ) }$

Find the one-sided Laplace transform of $f ( t ) = e ^ { - 2 ( t + 1.5 ) } u ( t + 1.5 )$

Find the inverse Laplace transform of $F ( s ) = \frac { 6 s + 15 } { ( s + 3 ) ^ { 2 } ( s + 5 ) ^ { 2 } }$

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Exam 14: The Laplace Transform

Find the inverse Laplace transform of F(s)=0.97s(s2+0.8s+0.97)F ( s ) = \frac { 0.97 } { s \left( s ^ { 2 } + 0.8 s + 0.97 \right) }F(s)=s(s2+0.8s+0.97)0.97​

Find the one-sided Laplace transform of f(t)=u(−t+8)f ( t ) = u ( - t + 8 )f(t)=u(−t+8)

Find the one-sided Laplace transform of f(t)=e−2t+10u(t−4)f ( t ) = e ^ { - 2 t + 10 } u ( t - 4 )f(t)=e−2t+10u(t−4)

Find the initial value and the final value of f(t) if F(s)=s+15s2(s2+4s+12)F ( s ) = \frac { s + 15 } { s ^ { 2 } \left( s ^ { 2 } + 4 s + 12 \right) }F(s)=s2(s2+4s+12)s+15​

Find the one-sided Laplace transform of f(t)=e−(t+2.5)u(t+2.5)f ( t ) = e ^ { - ( t + 2.5 ) } u ( t + 2.5 )f(t)=e−(t+2.5)u(t+2.5)

Find the one-sided Laplace transform of f(t)=7cos⁡(3t)u(t)+4sin⁡(3t)u(t)f ( t ) = 7 \cos ( 3 t ) u ( t ) + 4 \sin ( 3 t ) u ( t )f(t)=7cos(3t)u(t)+4sin(3t)u(t)

Find the inverse Laplace transform of F(s)=16(s+1)(s+2)(s2+4s+20)F ( s ) = \frac { 16 ( s + 1 ) } { ( s + 2 ) \left( s ^ { 2 } + 4 s + 20 \right) }F(s)=(s+2)(s2+4s+20)16(s+1)​

Find the one-sided Laplace transform of f(t)=u(t)−3u(t−2)+7u(t−5)−4u(t−7)f ( t ) = u ( t ) - 3 u ( t - 2 ) + 7 u ( t - 5 ) - 4 u ( t - 7 )f(t)=u(t)−3u(t−2)+7u(t−5)−4u(t−7)

Find the inverse Laplace transform of F(s)=3s+25(s+5)2(s+7)F ( s ) = \frac { 3 s + 25 } { ( s + 5 ) ^ { 2 } ( s + 7 ) }F(s)=(s+5)2(s+7)3s+25​

Find the one-sided Laplace transform of f(t)=5sin⁡(2t−π4)u(t)f ( t ) = 5 \sin \left( 2 t - \frac { \pi } { 4 } \right) u ( t )f(t)=5sin(2t−4π​)u(t)

Find the initial value and the final value of f(t) if F(s)=s+12s(s2+2s+8)F ( s ) = \frac { s + 12 } { s \left( s ^ { 2 } + 2 s + 8 \right) }F(s)=s(s2+2s+8)s+12​

Find the inverse Laplace transform of F(s)=2s+5s2+s+1.06F ( s ) = \frac { 2 s + 5 } { s ^ { 2 } + s + 1.06 }F(s)=s2+s+1.062s+5​

Find the one-sided Laplace transform of f(t)=(t+3)u(−t+6)f ( t ) = ( t + 3 ) u ( - t + 6 )f(t)=(t+3)u(−t+6)

Find the inverse Laplace transform of F(s)=s2+6s+18s(s+3)(s+7)F ( s ) = \frac { s ^ { 2 } + 6 s + 18 } { s ( s + 3 ) ( s + 7 ) }F(s)=s(s+3)(s+7)s2+6s+18​

Find the one-sided Laplace transform of f(t)=e−2(t+1.5)u(t+1.5)f ( t ) = e ^ { - 2 ( t + 1.5 ) } u ( t + 1.5 )f(t)=e−2(t+1.5)u(t+1.5)

Find the inverse Laplace transform of F(s)=6s+15(s+3)2(s+5)2F ( s ) = \frac { 6 s + 15 } { ( s + 3 ) ^ { 2 } ( s + 5 ) ^ { 2 } }F(s)=(s+3)2(s+5)26s+15​

Voltage, Current, Power, and Sources

Circuit Laws

Circuit Analysis Methods

Circuit Theorems

Operational Amplifier Circuits

Capacitors and Inductors

RL and RC Circuits

RLC Circuits

Phasors and Impedances

Analysis of Phasor Transformed Circuits

AC Power

Three-Phase Systems

Magnetically Coupled Circuits

Circuits Analysis in the S-Domain

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Find the inverse Laplace transform of $F ( s ) = \frac { 0.97 } { s \left( s ^ { 2 } + 0.8 s + 0.97 \right) }$

Find the one-sided Laplace transform of $f ( t ) = u ( - t + 8 )$

Find the one-sided Laplace transform of $f ( t ) = e ^ { - 2 t + 10 } u ( t - 4 )$

Find the initial value and the final value of f(t) if $F ( s ) = \frac { s + 15 } { s ^ { 2 } \left( s ^ { 2 } + 4 s + 12 \right) }$

Find the one-sided Laplace transform of $f ( t ) = e ^ { - ( t + 2.5 ) } u ( t + 2.5 )$

Find the one-sided Laplace transform of $f ( t ) = 7 \cos ( 3 t ) u ( t ) + 4 \sin ( 3 t ) u ( t )$

Find the inverse Laplace transform of $F ( s ) = \frac { 16 ( s + 1 ) } { ( s + 2 ) \left( s ^ { 2 } + 4 s + 20 \right) }$

Find the one-sided Laplace transform of $f ( t ) = u ( t ) - 3 u ( t - 2 ) + 7 u ( t - 5 ) - 4 u ( t - 7 )$

Find the inverse Laplace transform of $F ( s ) = \frac { 3 s + 25 } { ( s + 5 ) ^ { 2 } ( s + 7 ) }$

Find the one-sided Laplace transform of $f ( t ) = 5 \sin \left( 2 t - \frac { \pi } { 4 } \right) u ( t )$

Find the initial value and the final value of f(t) if $F ( s ) = \frac { s + 12 } { s \left( s ^ { 2 } + 2 s + 8 \right) }$

Find the inverse Laplace transform of $F ( s ) = \frac { 2 s + 5 } { s ^ { 2 } + s + 1.06 }$

Find the one-sided Laplace transform of $f ( t ) = ( t + 3 ) u ( - t + 6 )$

Find the inverse Laplace transform of $F ( s ) = \frac { s ^ { 2 } + 6 s + 18 } { s ( s + 3 ) ( s + 7 ) }$

Find the one-sided Laplace transform of $f ( t ) = e ^ { - 2 ( t + 1.5 ) } u ( t + 1.5 )$

Find the inverse Laplace transform of $F ( s ) = \frac { 6 s + 15 } { ( s + 3 ) ^ { 2 } ( s + 5 ) ^ { 2 } }$